As I said earlier, the Epistles, for me, provide reasonably good evidence in favour of existence.
The writer is talking about someone. Who is it? That is arguably the key question, possibly effectively the only one in the end. That as far as we can reasonably tell, the letters were written not long after the supposed death of the supposed person being referred to is a big plus. 25 or so years would be nothing by the standard of attestations in ancient history. It would be almost contemporaneous, even though it's not quite.
Now, of course, there are all sorts of other possibilities. The writer could be talking about a celestial being (correction: an 'only ever' celestial being and not someone who had ever actually been on earth, since 'Paul' does obviously write about a celestial being) or he could have been talking about someone from the dim and distant past, or the letters could have been edited or even written later to make it look like he was talking about an actual person who lived recently, or 'Paul' may not have existed either, or he might have been a Roman spy, or.......
For me, in the end, and despite the shortage of biographical detail, there is still just enough in the epistles and enough reason to think it more likely they were written, by whoever, when it is generally agreed they were, to tip the balance slightly in favour of existence. Alternatives just aren't as parsimonious or coherent as explanations, imo. Some are just a stretch. A very appealing stretch, because hey, they make everything so much more interesting, possibly especially to those not enamoured by Christianity in the first place.
One thing I will say is that the person the writer of the epistles was (imo probably) writing about might have been very different from the person who later made it into the Gospels. Whoever 'Paul' was, I think it's possible he was only top guy in one (his, created by him) 'wing' of the early cult, and that there was an earlier, very small, more 'Judean, Jewish' wing in Jerusalem that 'Paul' was greatly at odds with, and may have more or less hijacked, or at least piggy-backed on, being the apparently ambitious narcissist that he seems to have been. And I think it's possible that the small, early, Jerusalem cult got more or less wiped out in the disastrous (for Judean Jews) war and in the destruction of Jerusalem in particular that very shortly followed, which may be why we are left today with the 'Pauline' (Hellenistic, diaspora) version, including, of course, the 4 canonical Gospels, not to mention Acts (of the Apostles).
We don't necessarily have to like anything about 'Paul', early Christianity or possibly even 'Jesus', just by thinking there was (probably) an actual cult-starter (nearly all cults have actual founders) just prior to 'Paul' who was a more-or-less-at-the-time insignificant Judean Jew in the 1st Century who met an untimely death. We can see it all as involving at least mostly stupidity, superstition, duping, chicanery, politics (possibly involving what we might today call Marxist tendencies, or at least nationalism) militancy, radicalism, possibly even insurgency, and so on and so forth. I'm not saying 'Jesus' (if he existed) had no redeeming features, but there don't have to be all that many, and possibly very few indeed, in some scenarios.
Some have suggested that if the early Judean cult followers were around today, they might look quite a bit like the Taliban. That may be going too far, but I personally don't think it's totally way off. Just look at what the zeitgeist was, what was going on in the country at that time. Heck, look at some of the names (Iscariot = Sicarii, quite possibly, see links below*). Also, he was supposed to have been crucified. That's quite something. Check out what the Romans usually crucified Jews for at that time (and don't do it by reading the Gospels, those other two guys either side of him, if they even existed also, were probably 'bandits' not mere petty thieves, and 'bandits' has particular connotations in that context, being a derogatory term for political rebels). The founder, whoever he was, may of course have been a relative moderate, by the standards of the time. There is evidence that some of these religio-political, anti-establishment (including anti-Jewish establishment) Jewish fringe cults/movements had in their hierarchy both a militant person and a preacher (see also: propaganda) person, not entirely like many religio-political movements since and even today, in secular terms (See: The IRA and Sinn Fein).
But at least do not confuse saying that some fanatical nutter may have been going about in Judea in the 1st C with necessarily saying anything much in favour of him or the woo, end-of-the-world-is-nigh cult he might have been part of.
*
https://en.wikipedia.org/wiki/Sicarii
https://en.wikipedia.org/wiki/Judas_Iscariot#Name_and_background