Did physical reality (spacetime) begin to exist?

Clarifying the question
Did the Universe—or all physical reality—begin to exist? Does the whole of spacetime have an interval prior to which no temporally located event can exist?
 Universe / Physical reality = def. All of contiguous space and time with its boundary points and contents.
 Begin to exist = def. A state of affairs begins to exist if and only if there is a timedependent state A, and at least one finite interval or point of time X, such that A does not occur prior to X.^{1}
 The idea here is that since there is a finite duration that A does not precede, A must have a beginning. The extra rigor here actually is necessary. One cannot simply say X begins to exist if (1) X’s has a finite past or (2) X’s has a pastboundary, nor (3) The number of events earlier than now are finite. These have various philosophical challenges, like making assumptions about the nature of events and being able to definitionally pinpoint a “first” moment of time. Included is the challenge of not definitionally implying God or abstract objects begin to exist, simply because time exists. Consider also:
Alexander Pruss and Joshua Rasmussen: “(Begins) A state of affairs s begins to obtain iff (i) there is a time at which s obtains, (ii) there is a finite interval of time U, such that there is no time prior to U at which s obtains, and (iii) s cannot obtain without metric time.” What is it for time to begin to exist?
William Lane Craig & James Sinclair: “Following Smith (1985), we can plausibly say that time begins to exist if for any arbitrarily designated, nonzero, finite interval of time, there are only a finite number of isochronous intervals earlier than it; or, alternatively, time begins to exist if for some nonzero, finite temporal interval there is no isochronous interval earlier than it.” [“On NonSingular Spacetimes and the Beginning of the Universe,” in Scientific Approaches to the Philosophy of Religion, ed. Nagasawa (Palgrave Macmillan, 2012), 99.]

Experts (cosmologists & philosophers)
First consider cosmologists. Few express certainty, and while some suspect or hope for an eternal universe, the trend is to grant that the cosmological evidence points favorably to a real beginning. For example, Lawrence Krauss (prominent atheist cosmologist, and author of a book that aims to render God superfluous [Title: “A Universe from Nothing”]) had a debate over William Lane Craig's argument from a beginning to God's existence. Still, this was confessed…
Lawrence Krauss: “…as I told him [Dr. Craig], I bet that the universe did have a beginning. That doesn’t bother me. In fact, I think that it’s more likely than not, although not required.” [ Transcript of “Life, the Universe, and Nothing (II): Why Is There Something Rather Than Nothing?” William Lane Craig vs. Lawrence Krauss (2013) [online]^{1}
Another example:Aron Wall (Studies quantum gravity and black hole thermodynamics as a Lecturer at the University of Cambridge): “What does Modern Cosmology have to say about this question? I think that Modern Cosmology gives a fairly clear answer: probably, but not almost certainly.” wall.org article
[Many more forthcoming.]
 Similarly,...
• Lawrence Krauss: “As I said the first night, if I were going to guess, I would guess that the universe had a beginning. Namely, space and time began.” [Lawrence Krauss vs William Lane  Is It Reasonable To Believe There Is A God  2013]
 Similarly,...

Spacetime expanded from SOME singularity (Big Bang or not)
The Universe expanded from a singular mathematical nothingpoint, literally called a singularity.
On this page we can explore four arguments:
 (General Relativity) GR’s Singularity BigBang model is true.
 (BGV Theorem) Spacetimes that expand on average all begin.
 (2nd Law) Total entropic decay has not arrived yet.
 (Generalized 2nd Law) Total generalized entropy has not maxed out yet.
This is relevant because,
“At this singularity, space and time came into existence; literally nothing existed before the singularity, so, if the Universe originated at such a singularity, we would truly have a creation ex nihilo” [J. Barrow and F. Tipler, The Anthropic Cosmological Principle (Oxford, 1986), 442.]^{1}
Wait, no,
 … Space has been eternally expanding (there is no pastboundary). [See response]^{2}
But so what? Plausibly…
 Expansion from a singularitybeginning is a nonevent. [Forthcoming]
 That is to say, “…the universe's beginning wasn't an explosion. It was closer to an unfolding, or creation, of matter, energy, time,—space itself.” [Luz Kruesi, “Cosmology: 5 Things you need to Know,” in Astronomy (May 2007): 31.]
 One might suggest that space has been eternally expanding, but in response, there is a theorem in place which proves that a Universe eternally inflating/expanding on average requires infinitelyfast travel

General Relativity's Big Bang from nothing model is true
General relativity is true or adequate, describing with sufficient accuracy the full birth and growth of space from a singularity.
See this page to analyze 3 arguments
This is relevant because,
“If we push backwards far enough, we find that the universe reaches a state of compression where the density and gravitational force are infinite. This unique singularity constitutes the beginning of the universe—of matter, energy, space, time, and all physical laws. It is not that the universe arose out of some prior state, for there was no prior state. Since time also comes to exist, one cannot ask what happened before the initial event. Neither should one think that the universe expanded from some state of infinite density into space; space too came to be in that event. Since the Big Bang initiates the very laws of physics, one cannot expect any scientific or physical explanation of this singularity.” [Bruce Reichenbach, “Cosmological Arguments,” in The Stanford Encyclopedia of Philosophy (2017)]
No,
But so what? Plausibly…

BGV: Past eternal expansion require impossible speeds
Any Universe eternally expanding on average ends up requiring the possibility of infinitelyfast (and therefore fasterthanlight) travel speeds for inertial objects. See experts on this, ^{1}, elaboration of the concept^{2}, and a simplified illustration ^{3}.
See this page to see details and see:
This is relevant because space has been expanding, and yet an object traveling infinitely fast in space is impossible. (It both produces philosophical absurdities and violates the causality principle in Einstein’s special relativity).
But so what? Plausibly… … [All forthcoming]
 Space has an infinite contraction phase (i.e. contracts on average).
 Space has cycled infinitely (i.e. is static on average).
 Space underwent timereversal from an infinite past (i.e. nonaverage expansion).
 The BGV theorem is widely accepted.
• Alexander Vilenkin: “It is said that an argument is what convinces reasonable men and a proof is what it takes to convince even an unreasonable man. With the proof now in place, cosmologists can no longer hide behind the possibility of a pasteternal universe. There is no escape: they have to face the problem of a cosmic beginning.” [Many Worlds in One (Hill and Wang, 2006), 176.]
• William Lane Craig & James Sinclair: “The Borde–Vilenkin–Guth (BVG) singularity theorem is now widely accepted within the physics community. As of this writing, it has gone largely unchallenged.” [The Blackwell Companion to Natural Theology (Blackwell, 2004), 142.]
• GottLi: “The question of firstcause has been a troubling one for cosmology. Often, this has been solved by postulating a universe that has existed forever in the past. Big Bang models supposed that the firstcause was a singularity… with a proper theoryofeverything, one could perhaps push through to earlier times. Inflation has solved some of these problems, but Borde and Vilenkin have shown that if the initial inflationary state is metastable, then it must have had a finite beginning also. Ultimately, the problem seems to be how to create something out of nothing.” [J. Richard Gott and LiXin Li, “Can the Universe Create Itself?” (1997), p.41]
• Audrey Mithani, Alexander Vilenkin: “Did the universe have a beginning? At this point, it seems that the answer to this question is probably yes. Here we have addressed three scenarios which seemed to offer a way to avoid a beginning, and have found that none of them can actually be eternal in the past. Both eternal inflation and cyclic universe scenarios have Hav > 0, which means that they must be pastgeodesically incomplete. We have also examined a simple emergent universe model, and concluded that it cannot escape quantum collapse. Even considering more general emergent universe models, there do not seem to be any matter sources that admit solutions that are immune to collapse." [Did the universe have a beginning?, http://arxiv.org/pdf/1204.4658.pdf]  We know this because any eternally inflating space would require infinitely fast travel. This is relevant because an object traveling infinitely fast in space is impossible, producing absurdities and violating the laws of relativity.
• James Sinclair: "Vilenkin affirms that any universe (including universes modeled by higher dimensional cosmology, pre–Big Bang cosmology, and so forth,) which, on average, expands has to connect, in a finite time, to a past boundary (pers. comm. with Sinclair, March 4, 2004).
• Alexander Vilenkin: "Our argument shows that null and timelike geodesics are, in general, pastincomplete in inflationary models, whether or not energy conditions hold, provided only that the averaged expansion condition Hav > 0 holds along these pastdirected geodesics. (Borde, Guth, & Vilenkin 2003, p. 3)39 A remarkable thing about this theorem is its sweeping generality. We made no assumptions about the material content of the universe. We did not even assume that gravity is described by Einstein’s equations. So, if Einstein’s gravity requires some modification, our conclusion will still hold. The only assumption that we made was that the expansion rate of the universe never gets below some nonzero value, no matter how small. This assumption should certainly be satisfied in the inflating false vacuum. The conclusion is that pasteternal inflation without a beginning is impossible. [Many Worlds in One (2006), 175).]  The BordeGuthVilenkin theorem proves any universe expanding on average, including PreBig Bang and higher dimensional cosmologies, has a beginning. It explains that if a universe could be expanding on average for a pastinfinity of time, then an impossible object would need to be: an inertial object moving at infinity speed—faster than the speed of light.
Here is a simplification: Imagine a huge helium balloon with stationary ants scattered around it. Suddenly, one flying ant tells his friend, “I’m racing to the tiptop to meet the queen!” His friend registers the flight speed as 4mph. However, the next ant he passes only registers his speed as 3 mph, and the next at 2 mph. What’s happening? The balloon is inflating! Similarly, in an inflating space, inertial objects (e.g. a bullet) are registered as slowing down relative to noninertial objects that are carried by space (e.g. galaxies). From this, we can prove all inertial objects have a finite past. If bulletlike are slowing down on average, then as you rewind the tape their speed is faster and faster. However, inertial objects can’t move infinitely fast. They can’t even move faster than the speed of light.
So, while inertial objects moving through inflating space for the entirety of the space’s existence is possible, it is impossible for an inertial object to have been moving through space for an infinity of time. Therefore, inflating spaces are not pasteternal.

Total entropic decay hasn't arrived yet
Although the 2nd law of thermodynamics says the total entropy of an isolated system can never decrease over time, the Universe's entropy in fact is far from its maximal amount; its useable energy is still winding down.
For example, consider 1 simple evidence:
 Stars are still burning.
This is relevant because, if the Universe were pastinfinite, the 2nd law of Thermodynamics demands that the universe would have already reached a state of thermodynamic equilibrium (“heat death”; no more useable energy).^{1}
 • Paul Davies: “The first is that the universe will eventually die, wallowing, as it were, in its own entropy. This is known among physicists as the ‘heat death’ of the universe. The second is that the universe cannot have existed forever, otherwise it would have reached its equilibrium end state an infinite time ago. Conclusion: the universe did not always exist.” [God and the New Physics (Simon & Schuster, 1983), 11.]
• Paul Davies: “[The idea] that the universe has always existed in one form or anotherruns into a rather basic paradox. The sun and stars cannot keep burning forever: sooner or later they will run out of fuel and die. The same is true of all irreversible physical processes; the stock of energy available in the universe to drive them is finite, and cannot last for eternity. This is an example of the socalled second law of thermodynamics, which, applied to the entire cosmos, predicts that it is stuck on a oneway slide of degeneration and decay towards a final state of maximum entropy, or disorder. As this final state has not yet been reached, it follows that the universe cannot have existed for an infinite time.” [“The Big Bang  And Before.” The Thomas Aquinas College Lecture Series, Thomas Aquinas College, March 2002. (As cited by Craig)]
• P. J. Zwart: “…according to the second law the whole universe must eventually reach a state of maximum entropy. It will then be in thermodynamical equilibrium; everywhere the situation will be exactly the same, with the same composition, the same temperature, the same pressure etc., etc. There will be no objects anymore, but the universe will consist of one vast gas of uniform composition. Because it is in complete equilibrium, absolutely nothing will happen anymore. The only way in which a process can begin in a system in equilibrium is through an action from the outside, but an action from the outside is of course impossible if the system in question is the whole universe. So in this future state of maximal entropy, the universe would be in absolute rest and complete darkness, and nothing could disturb the dead silence. Even if there would by chance occur a small deviation from the state of absolute equalization it would of itself rapidly vanish again. Because almost all energy would have been degraded, i.e. converted into kinetic energy of the existing particles (heat), this supposedly future state of the universe, which will also be its last state, is called the heat death of the universe.” [About Time (NorthHolland, 1976), 136.] (As cited by Craig)]

Total generalized entropy has not maxed out yet
The 2nd Law of thermodynamics applies to black holes and similar types of horizons (hence the “Generalized 2nd Law”), suggesting that even in a quantumgravity context (like the Planck era), the conclusion of the Penrose singularity theorem applies.^{1} This is relevant because...
 Aron Wall (Studies quantum gravity and black hole thermodynamics as a Lecturer at the University of Cambridge): “…it strongly suggests that either the universe had a finite beginning in time, or else it is spatially finite and the arrow of time was reversed previous to the Big Bang [i.e. tornadoes put houses back together, and eggs unscrambled themselves]. In the latter case, it could still be said that the universe had a beginning in a thermodynamic sense, because both branches of the cosmology would be to the thermodynamic future of the Big Bang” [Classical and Quantum Gravity Vol 30 No 16 (2013), p.27 on arXive.]
 So see Aron Wall's paper, “The Generalized Second Law implies a Quantum Singularity Theorem).” in Classical and Quantum Gravity Vol 30 No 16 (2013)] (Updated 2016).

Logically, the past must be finite
Using pure a priori reasoning, we can discern that the number of previous events up until now needs to be finite in number, meaning there was inevitably a first event.
See this page to explore two arguments:
This is relevant because if the number of previous events is finite, then tracing history backwards brings one to a beginning of the first event.

A beginningless universe model is true
A cosmic model is true wherein the contiguous whole of space and time lacks a beginning.
This page analyzes ten evidences: [All Forthcoming]
 The AguirreGratton Time reversal model
 The BaumFrampton Cyclic model
 The CarrollChen Reversed arrow of time model
 The GottLi model
 The HawkingHartle “no boundary” proposal
 The Lindetype “Eternal Inflation” model
 The Penrose Conformal Cyclic cosmology
 The Steinhardt/Turok Cyclic model
 The Vilenkin “Tunneling from nothing” model
 The String Landscape inflationary model
 [See more]
This is relevant because, “If we were able to construct a complete and compelling naturalistic account, the necessity of appealing to God would be diminished.” [Sean Carroll, The Blackwell Companion to Science and Christianity]