Peter was ‘born again’, with or without being the ‘first pope’ - and btw, the rock on which the church is built is Jesus Christ Himself.
‘Born again’ simply means having personally accepted the redemptive work of Jesus on the cross, His death and ressurection. That is what ‘believeth in Him’ means in John 3:16 - “For God so loved the world, as to give his only begotten Son: that whosoever believeth in him may not perish, but may have life everlasting.”
It has always seemed to me that the rock meant Peter, although I have seen contradicting opinions here. But what does it mean to build the church on Peter? The Peter of the Gospel is an imperfect man, but it is his reactions to his own failings, once he realizes them, that make him a holy man. Could be that part of the message here is that the rock that we always have is the ready forgiveness when we fail, along with the more superficial message that the church will always be built on imperfect men.
Jesus IS the Church, but He put Peter in charge of BUILDING it after His resurrection.
If Peter and the other Apostles DIDN"T go out and build the Church, what do you think would have happened???? It would have died out!