Paul did, and claimed to have met Jesus. So either he's a liar (hardly a surprising quality in a cult leader as we know from modern cult leaders) or someone resembling Jesus existed. I think the former substantially more likely given that the Jesus he claims to have met is absent from all contemporaneous documentation.
I'm afraid I'm I'd have to look up the literature about the historicity of Matthew, Mark, Luke and John and whether there is hard evidence to show that their purported authors were real people with those names who really wrote those texts. I don't know offhand. It's not a topic that's ever been of interest to me.
However I do know that all of the Gospels were written long after Jesus' supposed life and death. Hence they don't count as contemporaneous accounts even if you don't automatically discount them as historical evidence because they are religious manifestos and not historical records. They aren't eyewitness reports, they're collections of myths put together by people who weren't alive at the time the supposed events took place.
Paul did, and claimed to have met Jesus.
Er, no he didn't. He specifically did not claim this.
"Matthew", "Mark" and "John" were tags added later to those Gospels. "Luke" is traditionally attributed to Luke the Evangelist, a companion of Paul's, who wasn't an eyewitness to Jesus.
The gospels are dismal failures as history - even apart from the miracles described therein.
To break up the awkward silence at the start of a recent Overcoming Bias meetup, I asked everyone present to tell their rationalist origin story - a key event or fact that played a role in their first beginning to aspire to rationality. This worked surprisingly well (and I would recommend it for future meetups).
I think I've already told enough of my own origin story on Overcoming Bias: how I was digging in my parents' yard as a kid and found a tarnished silver amulet inscribed with Bayes's Theorem, and how I wore it to bed that night and dreamed of a woman in white, holding an ancient leather-bound book called Judgment Under Uncertainty: Heuristics and Biases (eds. D. Kahneman, P. Slovic, and A. Tversky, 1982)... but there's no need to go into that again.
So, seriously... how did you originally go down that road?
Added: For some odd reason, many of the commenters here seem to have had a single experience in common - namely, at some point, encountering Overcoming Bias... But I'm especially interested in what it takes to get the transition started - crossing the first divide. This would be very valuable knowledge if it can be generalized. If that did happen at OB, please try to specify what was the crucial "Aha!" insight (down to the specific post if possible).