If Jesus didn't exist, that would have been an excellent argument to make for those who wished to snuff Christianity out from the beginning. Strange that the Pharisees and their religious descendants, the rabbis of the Mishnah and Talmud, never made that argument, although they had plenty of other things to argue about with the growing Christian movement. The rabbis disputed that Jesus was the Messiah, and they disputed that he was resurrected, but they did not dispute his existence. What an opportunity they missed, if this were true!
I would recommend the book _Jesus Within Judaism: New Light from Exciting Archaeological Discoveries_ by Professor James H. Charlesworth
(Doubleday, 1988) It contains a particularly interesting discussion of the "Testimonium Flavianum," the Josephus statement about Jesus, including an Arabic version of that statement wherein "blatantly Christian passages in the Greek are missing." Comparing the Greek and Arabic versions, it is very likely that Josephus did mention Jesus: The Arabic version says: "At this time there was a wise man who was called Jesus. His conduct was good, and he was known to be virtuous. And many people from among the Jews and the other nations became his disciples. Pilate condemned him to be crucified and to die. But those who had become his disciples did not abandon his discipleship." (page 95)
Thus, it cannot be stated categorically that Josephus did not mention Jesus. But more importantly, the rabbis of the Mishnah and Talmud did do so, and they never once used the argument that the antagonistic sect of Christianity was based upon a lie because there was no Jesus.
Further, using the same logic, we could argue that Josephus did not exist, since he is not mentioned in the New Testament, whereas non-Christian people, including even poets, are mentioned and quoted.
I will have no more to say on this, since argument leads nowhere. People will believe what they want to believe, and I certainly believe in Jesus. There are those who deny the existence of Abraham, Moses, David, Solomon and everyone else they want to deny. But the existence of the Jewish people gives life to the myth, if it is such. Likewise, for me, regardless of those who deny the existence of Christ (and probably Peter and Paul, too), the existence of the Christian congregation gives life to the myth, if it is such.
To each his own.