When Paul was young, things were magic. The car got him to school by magic. The stove magically warmed his food. And it was magical the way the rain fell from clouds.
Magic for Paul was just the yet unexplained. As he grew, Paul began to understand what made the car go, the stove heat, and the rain fall. There was a reason things happened, a method to them.
Somewhere in that lifetime Paul found out about God. No one knew when Paul gained a testimony, least of all Paul. He didn't need one of those "burning in the bosom" events to know what was right, he just knew. It made sense, it sounded right, in a way only real truth can.
Not content to learn things line upon line, Paul always wanted more. He yearned for that perfect knowledge God promises to all who seek it. And Paul sought it.
Now, you may wonder why Paul didn't always belong to the true church. I don't mean he wasn't baptized, I mean he didn't belong. Maybe it was because people stopped fellowshipping him. Some accused him of being a bible-basher. Most just thought Paul could kill a testimony with analysis. They threw their hands up in despair and said Paul had an "intellectual testimony". But they were wrong. People like Paul are often misunderstood.
Don't underestimate the power of a testimony, "intellectual" or not. God loved Paul and Paul loved God right back. Paul's testimony was never any stronger or weaker than those with "burning bosoms." When he testified of a truth, the Spirit confirmed it to him, just like it did to everyone else. And when Paul said, "I'm in the right place," the bosom burners didn't get it ...
Paul was sharing his testimony.