On the contrary, I would say there is plenty of evidence about Jesus that would be admissible, and allow us to build up a reasonable picture of his life. These would include the following:
I) he was born a few years BC. Both Luke and Matthew agree on this, and so does John. It's true Luke has another date reference (the notorious census) but this is inconsistent with what he says elsewhere and thus can fairly be regarded as some sort of slip.
Actually, neither Paul nor Mark have a birth at all, and the only two that were arbitrarily chosen as canonical guess wildly different years. And generally others guess even more wildly differently. Sorry, that doesn't sound to me like much evidence.
Plus, it all hinges on deciding that some uncorroborated propaganda documents are actually good evidence. By that standards, Captain Kirk has been... err... will be born in 2233, because Star Trek said so. That's not even a random example, but most of what they think they know about Jesus's life IS based on taking some stories from the OT as prophecy. Well, then I'm taking Star Trek as prophecy
II) he was born in Nazareth, but his mission was centred in Capernaum a few miles away.
And Captain Kirk is born in Riverside, Iowa. Actually here we even have better evidence for Kirk, because we even have a monument in his home town
Actually, even more so, because at that point you don't even have any actual "evidence" to base it on. Mark doesn't say Jesus was from Nazareth, Matthew and Luke have him born in Bethlehem, and at that Matthew seems to say that Jesus's parents were in Bethlehem all along and only moved to Nazareth much later.
And again, it's a move that is justified by fulfilling a "prophecy" (read: disparate phrase in the OT that only a schizophrenic would take as a hidden reference) rather than knowing anything. If that's good admissible evidence, then I'm the pope.
III) he was a disciple of John the Baptist. Interestingly, just beneath the surface, the Synoptics tie themselves in knots trying to get around the fact that their ministries overlapped, and thus were probably seen as rivals in some sense (the Synoptics want us to believe that Jesus did not start his ministry until the arrest of John).
Again, that's a claim that comes from one highly-biased religious document, and they did have one of those "prophecies" that said someone else will pave the way for the messiah. Plus, generally, if you wanted to at least try to sell that snake-oil to more Jews, trying to connect it to a recent super-star preacher is exactly what you'd expect a snake-oil peddler to do. Doubly so when they inherited a baptism ritual from Paul anyway, so it's not like connecting it to JTB comes out of nowhere.
There is also no real evidence that there was any rivalry, as opposed to just being Mark's getting the timeline wrong for his made-up fiction. That's just confabulating.
IV) his mother was called Mary, and he had several brothers (most likely). There is no reason to think his father was not called Joseph although he doesn't feature in any way after the birth narratives.
Right, and Luke Skywalker's mom was Padme Amidala, because St George Lucas says so
Mary is first named by Mark in 6:3, which tells us where everyone else got that. There is absolutely no corroboration to say that it had to be a real person, as opposed to just naming a secondary character, something done by every fiction author ever.
V) he had a somewhat peripatetic ministry in Galilee. This consisted of preaching and acts fully consistent with those of a folk healer/exorcist. His preaching was both apocalyptic (in the technical sense) and also squarely within the prophetic tradition as reflected in eg the Minor Prophets of the OT. Some of his rabbinic disputes about the interpretation of the Law with the Pharisees have been preserved (eg the Peah dispute about gathering corn from the corners of fields on a Sabbath).
Right, and Captain Kirk's actions are consistent with what we'd expect from a starship captain
Except for Jesus they're not entirely consistent. Even the imminent apocalypse theme is absent for example in the Q episodes, or in Thomas. His ministry is more in Judaea for Mark, more in Galilee for Q. His answers don't form a coherent position, but are all over the map in the whole genre of sayings attributed to him (e.g., some are a die-hard Sadducee position, some are so liberal that even the Pharisees balk, some seem more in line with various schools of hellenistic philosophy, etc), and most only work because the author says so.
Plus, again, there is no corroboration. You find evidence of Jesus only if you already decide that there was one, that the gosples preserved.
VI) he had a group of disciples, only some of which remained of importance after his death (yes, he died!

)
And Captain Kirk had several crew members, and only some remained of importance after his death. E.g., Spock is still a major figure centuries later, in the timeline of Star Trek Online
VIi) although he had probably been there before (even the Synoptics have Jesus having friends in Bethany, after all) he ended up in Jerusalem during the tumultuous Passover week of (probably) 33AD.
Except again we're moving from the domain of what even that pseudo-evidence actually says, to personal confabulation. Even his having any actual friends in Bethany only really appears in John, as a setup for a miracle. Mark, from which the other two synoptics copied doesn't actually say so. (Check out Mark 11 and 14.)
Plus even the dating is actually based on some 3'rd century astrological considerations, and is going against the "evidence" that those synoptics give. In fact, from being a ministry that starts after John The Baptist is arrested and summarily executed, it is now moved to something that started and ended while John The Baptist was still at large.
That's not having evidence, that's going against the "evidence."
VII) he was, to coin a phrase, crucified under Pontius Pilate after having been arrested as a result of an incident in the temple.
An incident in the temple which
A) couldn't really have happened by some lone nutter with a couple of disciples, because it was a very large surface full of thousands of people and guards that were there to prevent exactly that kind of thing, not to mention Pilate being there in town for the occasion with at least one cohort of highly trained soldiers, and
B) would have been written about if it did. We're talking an attack and disruption on a major government institution. And
C) if Jesus did get arrested for it, it would be on the spot, thus we'd have no Lord's Prayer and no last supper, contradicting not only the gospels but Paul too. (The last supper is actually pretty much the only thing that Paul actually tells us about what Jesus ever did except die.)
There really are no two ways around this. A lone Jesus or small enough group to not even be worth noting by anyone writing at the time, wouldn't even be a disturbance, and if it were criminal (like, say, the armed assault that John makes it be), Jesus and his gang wouldn't even exit that courtyard other than dead or in custody. Not only a group of 13 people (let alone a lone kung-fu master Jesus) wouldn't really overpower the guards and the hundreds of merchants, but by the time they were done there, they'd have to deal with the wall of shields and gladii of Pilate's soldiers. And if Jesus did bring enough people to take over the temple in no time and get the f-bomb out before the Romans get their kit on, you'd think someone would notice such a big attack on a major government institution. Like, say, Josephus.
The only way you can have a last supper after that is if, in fact, there was no real disturbance in the temple, or at least certainly not one worth the whole covert op to get him, convoking the Sanhedrin on Easter Friday, etc. Maybe a nutter Jesus did start shouting that everyone get out, but even that must have stopped quite short of being enough of a nuisance, or the priests would have told the guards to get him right there and then.
Isn't that quite of detail about an obscure 1st century figure?
The real point is that none of that is corroborated by anyone else, nor do we have any real reason to take some stories that miraculous and propagandistic as evidence. By that standard of evidence, Kim Jong Il managed 11 holes-in-one on his first golf game, because his propaganda says so. (And at that, never defecated.) But there is no sane reason to believe that any of that is true.