Hey butting in again.
I don't think one should try to pin down "when" the new birth takes place. It is by it's nature, a supernatural event wrought out by God. No one can know for sure, how far in advance this birth takes place of one hearing the message and beginning their conversion experiences. Some think it might be days, some think it might be nanoseconds before a genuine conversion begins.
What we do know about Saul is, he hated the church and Jesus Christ. But at the moment Christ came upon him, Saul called him "Lord". Was Saul prepared beforehand by the new birth like Lydia?
Acts_16:14 And a certain woman named Lydia, a seller of purple of the city of Thyatira, one that worshipped God, heard us: whose heart the Lord had opened to give heed unto the things which were spoken by Paul.
Or - in Saul's case, was it instantaneous with his meeting the power and Glory of the Lord. After all, the Second Person of the Godhead is quite capable of quickening an individual. There is no way to be sure. What we do know - it was private. Those traveling with him, did not hear are understand what was happening.