The faith that we place into trusting Jesus as our Lord is not produced within us, as that has to be given to us by God Himself!
Yes, everyone who believes in Christ has had that taught to them by the Holy Spirit, so it is gifted to them, without which they could not believe at all. It also begs the question who is being taught. As in are all taught or are only those God has chosen to know the truth are the ones He teaches.
John 6 easily tells us the answers, if we simply believe what Christ says. Christ negates all other alternative views in verse 64-65 as those who depart the faith as unbelievers God has not granted them to come to Christ.
64 But there are some of you who do not believe.” For Jesus knew from the beginning who they were who did not believe, and who would betray Him. 65 And He said, “Therefore I have said to you that no one can come to Me unless it has been granted to him by My Father.”
66 From that time many of His disciples went [p]back and walked with Him no more. 67 Then Jesus said to the twelve, “Do you also want to go away?”
68 But Simon Peter answered Him, “Lord, to whom shall we go? You have the words of eternal life. 69 Also we have come to believe and know that You are the Christ, the Son of the living God.”