For Iron Man, who breaks steel with his bare hands

This happened a long time ago. There is no video and no voice recording. The Bible wasn't written until the third or fourth century. You're talking about miracles. Besides, David Hume proved that extraordinary events require extraordinary proof, and you just don't have the proof.

Instead of following the rules of logic on this page, we treat the Bible as a historical document and look for the best explanation for the most significant historical event. To evaluate this, we look at the writing's date, description of the event, and, importantly, eyewitness accounts. 

Biblical scholars, including skeptics and non-believers, generally accept Paul's writings more than those of the other writers. Paul was well-educated, hated Christianity and Christians in his earlier life. Prior to his conversion, he did his best to destroy it. He hunted down Christians, had them tortured, and probably approved of their execution.

Something big-time happened. He claims he saw Jesus in the flesh 

In studying history, the time from the event to its recording is more significant than the time elapsed from the event to the present day. Within five years after the resurrection, the Apostle Paul traveled to Jerusalem to visit Peter and James. This visit is recorded in Galatians 1:18, and it is agreed that this event occurred within two to five years after the resurrection. During the visit, what he learned from the event was recorded by Paul in Corinthians.

What he learned from the visit is recorded in I Corinthians 15: 3-8: "For what I received I passed on to you as of first importance: that Christ died for our sins according to the Scriptures, 4 that he was buried, that he was raised on the third day according to the Scriptures, 5 and that he appeared to Cephas,[b] and then to the Twelve. 6 After that, he appeared to more than five hundred of the brothers and sisters at the same time, most of whom are still living, though some have fallen asleep. 7 Then he appeared to James, then to all the apostles, and last of all he appeared to me."

Note the rhythmic nature of the verses; it is not Paul's writing style. This information was easily memorized by those who could not read and shared with others who could not read. It would have been spread orally before being shared with the Apostle Paul.