You are raising the old issue of free will vs. election, over which wars have been fought.
In my view, the Bible teaches both. How could both be true simultaneously? In our three space and one time dimensions, they cannot, which is why we cannot understand it, being thus limited. But God exists in at least nine space and two time dimensions, wherein they can. In fact, there are about a dozen Bible verses in which both are taught in the very same verse.
The most obvious example of the situation you cite is Paul, whom God completely overwhelmed near Damascus. It might seem as though Paul had no say in his conversion. But at what point did Paul actually believe? It was after:
* he had spent time with many believers and had seen firsthand their faith under his duress
* his intense encounter with Jesus
* Ananias reported God's instructions to heal him and then the healing itself
Even when it appears God finds it needful to overwhelm, He is still providing evidence upon which to base a rational decision.
This Scripture came to mind. 2 Peter 3:9
https://www.biblegateway.com/verse/en/2%20Peter%203:9
Thank You Dan and Maudeen; good answers -