Since faith is merely trust in something, Jesus didn't give Peter anything, Peter's trust was not fully in Jesus.
The spiritual gift of faith spoken of to the church (who are already believers) is a separate issue.
There is also the question of when was Peter saved? Many scholars have debated when the apostles were saved, anywhere from following Jesus to after Christ rose from the grave.
Exactly. No believer had the indwelling Holy Spirit until after Jesus ascended. The apostles did not receive the Holy Spirit until after Jesus had risen, ascended, and then returned and breathed the Holy Spirit into them.
Jn 20:22 And when he had said this,
he breathed on them, and saith unto them, Receive ye the Holy Ghost:
We know that the disciples all believed (except Judas) from the beginning of his ministry.
Jn 2:11 This beginning of miracles did Jesus in Cana of Galilee, and manifested forth his glory;
and his disciples believed on him.
This was at the wedding where Jesus turned the water into wine. All of his disciples believed on him when they witnessed this miracle except Judas.
If a man must be regenerated by the Holy Spirit to be enabled to believe, how did Jesus's disciples believe on him? They did not receive the Holy Spirit until John chapter 20 when Jesus breathed on them after his resurrection.
And the scriptures show that all the people (and there were multitudes) that believed on Jesus did it without the indwelling Holy Spirit in John chapter 7.
Jn 7:37 In the last day, that great day of the feast, Jesus stood and cried, saying, If any man thirst, let him come unto me, and drink.
38 He that believeth on me, as the scripture hath said, out of his belly shall flow rivers of living water.
39
(But this spake he of the Spirit, which they that believe on him should receive: for the Holy Ghost was not yet given; because that Jesus was not yet glorified.)
Only a few select men in the OT had the Holy Spirit, though many thousands believed. When Jesus preached, many thousands believed on him, yet they did not receive the Holy Spirit until after Jesus was glorified.
So, if a man must be regenerated to have the ability to believe, how did all these people believe (and the scriptures clearly say they did) without the Holy Spirit?