God gives faith, but He does not do the believing. We are commanded to believe.
Somewhere in between 1. God giving faith to a person . . . . . and 3. that person being saved by God is 2. the person's responsibilty to believe and his believing.
God does believe on behalf of someone. The person believes.
We are called to believe because in that belief we turn from our own righteousness to His. That is the purpose of belief, not a condition for being saved.
God saved the Israelites out of Egypt before they believed, but when it came time for them to believe He destroyed those who did not.
Exodus 32
33 But the LORD said to Moses, "Whoever has sinned against me, I will blot out of my book.
34 But now go, lead the people to the place about which I have spoken to you; behold, my angel shall go before you. Nevertheless, in the day when I visit, I will visit their sin upon them.
God gives us the ability to believe just like He did the Israelites. If we turn from Him after that, in unbelief, and turn to believe in something else - like the people did the calf - then it's our choice to leave and not believe in Him.
Exodus 32
1 When the people saw that Moses delayed to come down from the mountain, the people gathered themselves together to Aaron and said to him, "Up, make us gods who shall go before us. As for this Moses, the man who brought us up out of the land of Egypt, we do not know what has become of him."
2 So Aaron said to them, "Take off the rings of gold that are in the ears of your wives, your sons, and your daughters, and bring them to me."
3 So all the people took off the rings of gold that were in their ears and brought them to Aaron.
4 And he received the gold from their hand and fashioned it with a graving tool and made a golden calf. And they said,
"These are your gods, O Israel, who brought you up out of the land of Egypt!"
5 When Aaron saw this, he built an altar before it. And Aaron made proclamation and said,
"Tomorrow shall be a feast to the LORD."
6 And they rose up early the next day and offered burnt offerings and brought peace offerings. And the people sat down to eat and drink and rose up to play.
These people purposefully turned from God, who had saved them, and deliberately made gods to worship. They called on it as their Lord.
Everyone has a Lord. They either obey and follow the true God, or they obey and follow a false one.
A person may say that Jesus is Lord, but if He is not then just saying He is does not make it so anymore than Arron declaring that golden calf was.
God blotted those who sinned in this manor from His book. He will do the same for those who turn away from Him today.
Revelation 3
2 Wake up, and strengthen what remains and is about to die, for I have not found your works complete in the sight of my God.
3 Remember, then, what you received and heard. Keep it, and repent. If you will not wake up, I will come like a thief, and you will not know at what hour I will come against you.
4 Yet you have still a few names in Sardis, people who have not soiled their garments, and they will walk with me in white, for they are worthy.
5 The one who conquers will be clothed thus in white garments, and I will never blot his name out of the book of life. I will confess his name before my Father and before his angels.
6 He who has an ear, let him hear what the Spirit says to the churches.'