Faith is not self-confidence. Biblical faith is not mere orthodoxy - that is, believing correctly with our minds the right doctrines of the Bible. The Bible says that mere orthodoxy alone will qualify us to be like demons. Demons are orthodox. Demons believe in God.
Demons believe in biblical doctrines.
But that doesn't make demons able to see or enter the kingdom of God. Secondly, let me say to you again that faith, like repentance, is the fruit of regeneration, not the cause of it. It is the other way around. Just like repentance is the fruit of regeneration, faith is the result of regeneration. It is the gift of God.