Jesus explicitly teaches that regeneration precedes faith:
"The Spirit quickens [regenerates], the flesh counts for nothing...that is why I told you that no one can come to me unless the Father who sent me grants it." John 6:63, 65
In the same context Jesus declares, "All the Father gives me will come to me..." - John 6:37
"All", not some. All the Father gives the Son will come to Him. And the "giving" of the Father to the Son precedes their coming to faith in Him.
The words "grant" (v 65) and "give" (v 37) are the same Greek word.