I think first of all of what Jesus said in John chapter 3, when he said to Nicodemus that unless you’re born from above—which is regeneration—you’ll neither be able to see or enter the kingdom of God (John 3:3-5). And we enter the kingdom of God through faith.
So in that conversation, I think it’s very clear that in order to come to faith, first of all, God has to give us a new heart. And that is really what John had said in the prologue to the gospel as well, that those who came to believe in Him were born not of the will of the flesh or the will of man, but born of God (John 1:13).
So when we’re thinking about it, we realize that, logically, regeneration grounds our faith. But when we are regenerated, we come to believe.
So there is not a gap that we would be able to detect between being born again and coming to believe. In fact, the way we would recognize that we had been born again was because that came to expression in our trust in Jesus Christ. So they are very intimately related.