There is, regrettably, no direct and unambiguous evidence. There is circumstantial and tangential evidence. Aahmused's review is very good at discussing near-contemporaries or contemporaries.
It makes sense that the contemporaries of Jesus would not talk about him much. He was a very minor, esoteric rabbi who got politically executed just as he was becoming potentially very important. It was his teachings through his disciples that mattered.
But it would be very strange if the man had not existed. Paul was a near-contemporary, and while he didn't meet the man himself, it would be pretty noteworthy if no one had ever even seen the guy. And I suspect that if the Romans could have disproved that Jesus existed at all by producing legal transcripts and eyewitness reports, they would have.