Prior to to the start of Jesus' ministry, God sent prophets to deliver messages to mankind. Of those prophets, only a few ever saw Jesus: Moses and Elijah (at Jesus' transfiguration), John the Baptist (whom Jesus called the greatest of the prophets), Anna and Simeon. Yet Christians still give careful thought to what the others wrote: Isaiah, Jeremiah, Daniel and the rest.
As a commenter said, Paul claimed to have seen the risen Jesus, and this was confirmed by a vision to Ananias of Damascus in Acts 9:10-16. The importance of this witness is vital. This man was fearful of Paul and knew his reputation and the purpose of his mission to Damascus - to seize Christians to be imprisoned or worse. Ananias had no motive to accept Paul and plenty of reasons to reject him. The fact that Ananias received Paul and protected him is proof of the divine approval of Paul's apostleship.
A second endorsement in Scripture comes from the Apostle Peter:
15 Bear in mind that our Lord’s patience means salvation, just as our
dear brother Paul also wrote you with the wisdom that God gave him. 16
He writes the same way in all his letters, speaking in them of these
matters. His letters contain some things that are hard to understand,
which ignorant and unstable people distort, as they do the other
Scriptures, to their own destruction. (2 Peter 3:15-16)
Peter here elevates Paul's words to the level of Scripture. Since the Catholic Church reveres Peter as the first Pope and the one entrusted by Jesus with leadership of the church, his endorsement is also significant.
Another endorsement is that of the Holy Spirit, who uses Paul's words in the lives of believers to bring spiritual blessing. I was delivered from years of depression through the book of Philippians. Other people have their own testimonies of the power of Paul's words. Martin Luther triggered the Protestant Reformation when the truth of one verse in Romans burst upon his consciousness.
One final endorsement comes from logic. If the Bible were missing something that adding Paul's writings corrected, what might that be? There is a word of vast importance that is found sparingly throughout the Bible but commonly in Paul's letters: peace. Paul uses the word peace as much as the next two prophets combined, and as much as all the other writers of the New Testament combined:
- Paul: 47 usages
- Isaiah: 25 usages
- Jeremiah / Lamentations: 17 usages
- Rest of New Testament: 46 usages
The fact that we can find peace with God through faith in Jesus Christ and his sacrifice upon the cross is the central message of the gospel. It shines brightest in Paul's words.