Jesus lived and worked among the poor, and such people seldom have their actions covered as well as emperors. It doesn't mean they didn't exist, though it places them outside history - in the sense of 'written history'. But anyone who wants to suggest that he never existed, and was just invented by Paul, needs to explain why If Paul, for some reason, wanted to instigate a new religion, why not just name himself as the prophet rather than invent one who'd supposedly died years before?
For me, that just doesn't make any sense. The likeliest explanation is that Jesus lived and preached and was remembered after his death, and that his teachings were handed down orally until people came to write them down. (Whether he was the son of God is another matter.)