[Note: I am only considering the letters of Paul where his authorship is not rejected by scholars, see texts.]
Paul explicitly claims that he knows Jesus Christ only through supernatural revelation and through reading the scriptures. Paul writes about other people having similar supernatural experiences with the resurrected Christ, but does not claim that anyone has interacted with Jesus in any other way.
You often hear mention of the fact that Paul doesn’t talk about the events of Jesus’ mortal life aside from the crucifixion — but it’s worse than that. Even when taking to or about people who should have learned from Jesus in person (or at least second-hand, through Jesus’ disciples turned apostles) — there’s no hint or mention of it.
Paul writes about meeting with leaders such as Peter and others in the Jerusalem church — claimed by the gospels to have been Jesus’ disciples in person for years — yet Paul explicitly says that he didn’t learn anything about Jesus from them.
The only thing Paul says that would place Jesus as his contemporary is his reference to James as “the brother of the Lord” (plus one similar reference to other “brothers of the Lord”). Obviously if he meant “brother” in the familial sense, then, by extension, he’s saying Jesus was a person who alive not too long ago. But it’s not clear that that’s what he meant.