From a human perspective, maybe it's as simple as Paul's transformative experience with Jesus on his Road to Damascus trip, which left him with zero personal doubts about who Jesus was. Jesus - resurrected, alive, and well - was an unquestionable fact. For Him, debating this might have been like wasting his time arguing with blue sky skeptics, in contrast with Paul offering his opinions on matters of early church life, where he is less certain and seems to offer practical life advice for early Christians. An example is 1 Corinthians 7:25–39.

But the answer may be in your question. We don't argue about whether the sky is blue because we all know it's blue. Paul may not have needed to defend Jesus because the general population in Judea believed Jesus existed and was resurrected, even when the political powers hunted, tortured, and killed followers of Christ. The life of Jesus was accepted knowledge. Whether they followed Him is a different question.