Did early Christians venerate Jesus' gravesite?

“Yes, after all…

No record/evidence exists for a Jesus-grave being venerated in the 1st century.¹ This is relevant because “Had such been the practice of the first Christians [for Jesus's tomb], with all the significance which the very practice itself presupposes, it is hard to believe that our records of Jerusalem Christianity and of Christian visits thereto would not have mentioned or alluded to it in some way or at some point.” [James Dunn, Jesus: The Evidence (Westminster, 1985), 67.]

Normally, for prominent ancient figures of this kind, we have such references to their tomb, and with respect to Jesus we especially have an abundance of early Christian information in which we would have expected references to turn up, if such a tomb were in fact venerated.²

• Byron McCane (Religion professor at Wofford): “…the earliest hints of Christian veneration of Jesus' tomb do not surface until the early fourth century CE. (Eusebius, Vita Constantini 3.25-32.)” [“Where No one Had Been Laid”, in The Historical Jesus, Vol 3, ed. Evans (Routledge, 2004), 268.]
• James Dunn (NT professor at Durham): “The fact remains that evidence for such interest in a tomb (whether empty or undisturbed) in the earliest decades of Christianity is wholly lacking.” [Jesus Remembered (Wm. B. Eerdmans, 2003), 837.]
For example, we have records/evidence for the veneration James's tomb (the brother of Jesus).
• A.J.M. Wedderburn (NT professor at Munich): “Although cultic veneration of hero's graves was well-attested in the Graeco-Roman world, we never read of any Christian veneration of that of Jesus. In contrast, that of his brother James was well-known, even if it was not a place of worship: around 180 CE Hegesippus records that James the Righteous had been buried near the Temple in Jerusalem and that his gravestone was still there.” [Beyond Resurrection (Hendrickson, 1999), 63.]