It's not a terribly good standard to begin with. We don't judge the existence of individuals solely on attribution by other sources. Paul's existence is quite firm from his Epistles, which early on in the Church had great authority and bare witness to an Early Church gathered around this person called Jesus.
If Paul didn't exist then who wrote the Epistles to the Churches in the name of Paul? What did they hope to accomplish? Even if we were to take the argument seriously that the Epistles themselves were not written my Paul they point to evidence of Paul existing and having great authority in the Church. If Paul didn't exist and these were forgeries then why write in the name of someone who had never actually been to and established these Churches? Would the letters of Paul have convinced anyone if that were the case?
The best evidence for Paul's existence is his own Epistles. We need not a third party to collaborate his existence, though the second century Church Fathers clearly do.