Were the AD 30 Jews saying body theft caused empty tomb

Introduction

In other words: In c. AD 30, were the Jerusalem Jews publicly maintaining that “the reason Jesus's body is gone from its tomb is because someone stole it”?

Relevance: This question plays a role in other debates, notably…
• …was Jesus's tomb empty?
• …was Jesus's corpse stolen?

“Yes, after all…

Matthew 28 says they did

In c. AD 75, Matthew reported that “From the get-go (AD 30), Jews were saying that 'body-theft explains the empty tomb.”¹

But so what, couldn't it simply be that Matthew (and/or his source) lied, not really believing that AD 30 Jews cried theft?²

Mt 28:11-14 -- some of the guard… reported to the chief priests [about gt (in AD 30). They responded], “You are to say, ‘His disciples came by night and stole Him away while we were asleep.’ …this story was widely spread among the Jews, and is to this day.
This is unlikely, for two reasons:
• First, Matthew (and/or his source) had reason to refrain from spinning such a lie.
◦They willed to report gospel-history honestly [Forthcoming]
◦Such a lie was stupidly falsifiable (such that, even if Matthew was spinning a lie, he would not spin the lie like that).
• Second, Christians like Matthew lacked reason to spin such a lie.
◦ Early Christians did not care to use an empty tomb as evidence for Jesus's resurrection.
◦ Additionally, such a lie would be too obviously unacceptable to the Jews who are supposed to believe it, and it would therefore be useless apologetics. (After all, the Christian obviously would not have expected readers who are skeptical of the empty tomb to be more inclined to accept that AD 30 Jews affirmed it!)

Those Jews were saying it in AD 75

By AD 75, Jews were affirming “body theft caused the tomb's emptiness” (to rebut “the empty tomb proves he rose!” apologetics). This is relevant because the AD 70 Jews had inherited their “theft” polemic from their AD 30 predecessors.¹

We know AD 70 Jews inherited their polemic from AD 30 Jews for five reasons:
• In c. AD 30, Jews formed some public rebuttal to the empty tomb. Critics might reply here that Christians were not much using empty tomb apologetics in AD 30-70. In response, however, a Christian can say: “So what? They were proclaiming Jesus's resurrection, and this could be more than enough for Jews to preempt apologetics, provided the Jews knew the tomb was empty.

William Lane Craig: “The proclamation may have been in the words repeated twice in Mt. 27.64; 28.7: 'He has risen from the dead.' Contrary to Grass, Ostergeschehen, p. 23, this could evoke the response that the disciples stole the body, if the empty tomb were also a historical fact. The Jewish response need not presuppose the Christians were using the empty tomb itself as an apologetic argument.” [“The Guard at the Tomb”, New Testament Studies 30 (1984)] • if Christians were only circulating an “empty tomb” proclamation much later (e.g. AD 70), Jews would've responded with a simple report: “What empty tomb!?” For example,
Robert Stein (NT professor): “[Even] If it had originated at a late date, there would have been no need to create such a polemic. At such a date one would have raised questions such as “What empty tomb? Where does this new claim that the empty tomb was empty, from? We have never heard anything about an empty tomb.” The fact that the Jewish polemic never contested the existence of the empty tomb indicates that this tradition is very old. Such a concession that assumes that from the beginning Christians proclaimed Jesus' tomb was empty. It probably also indicates that the Jewish leaders had in fact found it empty.” [Jesus the Messiah (IVP, 1996), 265.]

Richard Swinburne (Philosophy professor at Oxford): “…there would have been no need for the Jewish enemies to circulate the story that the disciples had stolen the body…; it would have been sufficient to refer to the obviously confused character of the Christian story [that the tomb was empty].” [The Resurrection of God Incarnate (Clarendon, 2003), 177.] A critic might also (erroneously) try to suggest that Jews lacked any real will/desire to impede Christianity. [Forthcoming] • There'd sooner/plausibly be evidence/traces of a different pre-AD 75 rebuttal circulating, if one existed. (But there isn't one!)
• The AD 75 Jewish rebuttal is most efficiently explained by saying they inherited directly it from their predecessors. This is relevant because, all other things being equal, simple explanations are to be preferred.
• No plausible explanation exists for why the allegedly different pre-AD 75 would be abandoned. By way of response, a critic might allege that Jews forgot their original rebuttal to empty tomb apologetics, but this seems unlikely. Jewish antagonists inside Jerusalem and outside of it would remember their original rebuttal to Jesus' allegedly empty tomb (even after 70 AD). After all, in addition to a surplus of survivors, the debate topic arose frequently enough to keep it in live memory.
• If Jews did not have a compelling reason to start crying “body-theft caused the empty tomb” in c. AD 30 (e.g. because they knew it was true, and that “theft” was the best rebuttal to its being used as proof for Jesus's resurrection), then they certainly didn't have a compelling reason after c. AD 30.