One of the Earliest Witnesses
Richard Carrier, refuting a similar argument from JP Holding, puts it best when he writes the following:
Why would he have persecuted them so vehemently if the evidence for the Resurrection was already as extraordinarily good as Holding's argument requires? Why does Paul only believe after he himself sees a vision of the Christ telling him he is wrong? Why does Paul never mention any other reason for converting? Even in Acts, he never cites any evidence as having convinced him, except his own personal vision (besides the scriptures, of course). He never makes any references to checking the facts of the empty tomb story, or being persuaded by the testimony of other witnesses--not even in Galatians. In fact, in Galatians Paul goes out of his way to deny having done any such thing until, at best, many years after he was already converted. So why did it take a personal visit from God to convince Paul? We cannot say he was loony or stupid--from his letters we can see Paul clearly was neither. There can be no plausible explanation for his not believing the Christians except the fact that he had no reason to believe them. Which entails there was no evidence that could be checked at all, or what could be checked was inconclusive to any reasonable man like Paul.
So contra Craig, Wright and Bauckham, we have multiple people who lived in Palestine around the time of the supposed resurrection and empty tomb, some of whom were referred to as Christians, who simply were not convinced by the evidence for the resurrection. The largest group who weren't convinced were the Jews, who simply saw no reason to believe this supposedly miraculous event took place even though they could also interview anyone involved. Paul was a member of this group before his vision on the road to Damascus and he was definitely not convinced by the evidence.
Therefore, the evidence wasn't convincing enough for Paul, who was alive and able to interview the supposed Christian eyewitnesses whose stories supposedly later became the Greek gospels. The only evidence that convinced Paul was a vision. If Paul had not had the vision, he would have continued to remain unconvinced, meaning there simply was not adequate physical or testimonial support for the belief in the resurrection prior to the time Paul had his vision.
This is a large problem for arguments such as William Lane Craig makes with his claims that the resurrection is the best explanation for the historical facts presented by the Greek gospels. Craig puts it this way in "The Historicity of the Empty Tomb":
Therefore, the Christian community also, of which Peter was the leader, must have believed in the empty tomb. But that can only mean that the tomb was empty. For not only would the disciples not believe in a resurrection if the corpse were still in the grave, but they could never have proclaimed the resurrection either under such circumstances. But if the tomb was empty, then it is unthinkable that Paul, being in the city for two weeks six years later and after that often in contact with the Christian community there, should never hear a thing about the empty tomb. Indeed, is it too much to imagine that during his two week stay Paul would want to visit the place where the Lord lay? Ordinary human feelings would suggest such a thing. So I think that it is highly probable that Paul not only accepted the empty tomb, but that he also knew that the actual grave of Jesus was empty.
However all Craig really has here is speculation and he fails to address the primary question of Paul's rejection of the evidence prior to his conversion. In addition, he simply glosses over the existence of the Ebionite community who considered themselves Christians yet rejected the bodily resurrection. For of course all of the chances to investigate the claims of Christianity were just as available to the Ebionites, Jews and Paul prior to his conversion. Furthermore, prior to that time Paul would have been approaching those claims with the doubts of a skeptic, rather than the beliefs of someone who had the fervor of a new convert.
To phrase the argument briefly then I would say this:
1. Prior to Paul's conversion, any evidence for the resurrection was just as strong as it was after his conversion.
2. The evidence for the resurrection failed to convince Paul of the truth of Christianity.
3. Therefore, the evidence for the resurrection alone, without specific interventions by God to make someone believe, must be inadequate to convince a skeptic who has not had a vision from God of its truth.