Ok. Then your first indication that the existence of Jesus would have been recorded if he really existed has no support.
Your second thesis was that Jesus was an invention of Sha'ul, Paul. I don't see a motivation for a Jewish Pharisee from the Greek diaspora to invent a story of a Messiah that lived a short time ago, a lapse of time that is short enough to have most people still living.
Why should he be so bold to invent a complete lie?
How should he make people believe him?
Why should he construct , nota bene before the destruction of the Temple of Jerusalem, a legend of the long awaited Messiah?