A Jewish historian & commentator in Rome named "Josephus" ("Joseph" plus a Roman suffix) wrote a section in one of his books describing several wandering Jewish doom preachers of that era who developed significant followings for a while. So the fact that guys like that existed in general is established by a non-Biblical source. But the individuals he describes are mostly too different from Jesus. For one thing, they had other names, or were identified only by where they came from but it wasn't where Jesus was from. (For example, he called one "The Samaritan", but Jesus was no Samaritan.) I think there was a "Galilean", but that's where we run into more substantial mismatches in what these guys did and preached, compared to what Jesus is supposed to have done & preached. For example, one of them led his crowd to the Jordan River expecting it to split open for them to escape across it. (It didn't.) But there are a couple who come close enough to have contributed to the later Jesus idea.
One was identified only as "The Egyptian", which already isn't a bad start because the Gospels have Jesus living in Egypt for a while as a child. And he centered his preaching on the Mount of Olives, and had a large enough following to annoy the Romans so they sent an army after them, resulting in what Josephus calls a battle/slaughter. That might seem to contradict the Jesus story, which we now tend to think of as a smaller-scale thing where a few guards/cops were sent to arrest an individual with relatively few or no other people around like in "Law & Order", but I've recently encountered an argument that the word that's used in the Gospels for that group of Romans was actually a military unit, a chunk of the army, so the Gospels really have Jesus captured by an army, just without depicting the rest of the battle around him. Whether that's a fair translation or not, the size of The Egyptian's following certainly sounds similar to the crowds that are depicted elsewhere in the Gospels, even if not for the arrest/capture scene. And after the chaos of a battle (especially one where one side was an undisciplined rabble), or a slaughter, or a riot getting squashed, most survivors wouldn't have known the fate of one individual, so it would have been easy to tell them whatever you wanted later on.
Another was actually named "Jesus", although from the wrong town and with the wrong father. He entered the city during a Jewish festival, went to the temple to rant against it while quoting Jeremiah 7, stuck around afterward to preach daily about the coming destruction there, was seized & beaten by Jewish authorities who accused him of speaking against the temple, offered no defense, was turned over to the Romans who beat him some more, was interrogated personally by the Roman governor, still offered no defense there either, and was not found guilty or dangerous and thus free to go by the governor, only to end up getting killed by Romans anyway, after crying out a final lament for his own sad fate. (It wasn't "why have you forsaken me" on a cross, though; his final quote simply switched his usual "woe to Jerusalem" and "woe to the temple" to "and woe to me as well", before getting konked in the head by a projectile during a siege.)
So we don't even need to be quite so vague as "well, there were these guys in general, and 'Jesus' was a common name". Most of what we would look for as an origin of the Jesus legend is already specified in just those two guys. (The only thing keeping me from saying Jesus was a real person would then be the fact that two does not equal one.

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