Jesus almost certainly existed. I know it’s fashionable among atheists to deny he existed (apparently Paul and Peter made him up from scratch?) However, I think this claim blatantly contradicts the evidence. First of all, “A Jewish cult leader named Yeshua” existed is not an extraordinary claim; there were plenty of similar cult leaders in Roman-era Judea. Secondly, if Jesus didn’t exist—where did his cult come from? Paul’s writings are the earliest Christian documents we have, from the 50’s AD… and at this time, there was already a well-formed cult of “Christians.” If Paul and Peter invented the person of Jesus, why was there already a cult centered around Jesus? It makes no sense; it’s much more in line with Occam’s razor to say they simply co-opted a cult that Jesus started (much like how Jesus perhaps co-opted John the Baptist’s cult).
As for Jesus dying on a cross—again, this is not an extraordinary claim. The Romans crucified thousands of people, especially people with political power. Sure, there’s no “proof” by modern standards—no photographs or eyewitness accounts—but then there isn’t a similar level of proof for almost anything from the ancient world. I see no reason to doubt that he was crucified.
by the way, “Jesus wasn’t crucified” is actually a sectarian religious claim. A sect of early Christians called the Docetics believed that Jesus only “appeared” to be crucified—that it was some kind of illusion on the cross, and he lived on. Interestingly, this story gets picked up by the Muslims and is alluded to in the Quran. I have a feeling that people making the claim that he wasn’t crucified are conflating the Docetics’ religious belief with an actually valid historical position.