Paul (Saul of Tarsus) never saw Jesus in the flesh or resurrected or in any tangible form. His claim to fame is having a vision of a bright light and hearing a voice just before he went into a 3 day coma while heading to Damascus (Acts 9:3-7).
About AD36, Paul had visited Peter and James in Jerusalem and learned of the legend there. Although he denied it (Gal 1:11-12), his testimony is second hand stories of whatever he heard from them.
While he was a energetic evangelical, Paul is a poor witness for Christ.
First, we do not know whether Saul saw Jesus before He died. Since Saul was politically active in Jerusalem it is likely that he was present for much of what happened to Jesus. Our first reference to Saul is that he was present at the stoning of Stephen, but that is only the first reference.
He also did not spend 3 days in a coma, but blind. He was alert for those three days.
You can ignore the claims in Galatians 1 if you wish, but they are entirely consistent with other claims of the apperance of the Resurrected Christ made at the time.
Shalom.