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
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
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.