I doubt this "he rose from the dead" business started until years later. The letters and gospels, we know, weren't written until decades after the crucifixion. Oh, they tell the story that "the women went to the grave 3 days later and lo! There was only an angel." But isn't this odd that this wasn't written down until any of those who could have been witnesses were safely dead and gone? I'm sorry, but the whole thing is obviously fiction, produced well after the fact, as a recruiting device.
Even if it was all written down after the witnesses were dead, it just doesn't make sense for it to be an invention. Unless all Christians signed on to the invention at once, there would have been "non-resurrectionist" Christians. At least at first, they would've been the majority. Why aren't there records of them? And don't say their works were lost or destroyed: most of modern knowledge of the Gnostics comes from anti-Gnostic polemics. The New Testament itself contains anti-Judaizer polemics (Galatians, for example). Now, there is a polemic passage about the resurrection in Scripture, I Corinthians 15. But it's a polemic for an eschatological resurrection
based on the resurrection of Christ. The resurrection of Christ was a given.
Among Christians, the resurrection has never been a new doctrine. Belief in the resurrection goes back as far as Christianity, regardless of when you think the NT was written.
The earliest NT fragments are from the late first century. Unless the earliest were from the autographs (highly unlikely, of course), they go back further. I find nothing unlikely about the texts' own claims that there were witnesses still alive.
Even if there weren't, at some point the doctrine was introduced, and not into a vacuum. If there weren't people who were in Jerusalem when things when down, there would have been non-resurrectionist Christians (as I pointed out above) and anti-Christians who would have seen the change in doctrine. If they saw any such change in doctrine, they never said anything about it.
All of which leads back to the question, where did belief in the resurrection come from, and if it's false why didn't someone either produce the body, point out there never was such a person as Jesus, point out the fact that the doctrine was just invented, or use any of the other conclusive counter-arguments that would've been there if the alternatives to the reality of the resurrection were true?