Choosing to/not to Believe? Not Possible?

[Fake Messiah]

Now this is very interesting to me because I have heard this argument from certain Christian denominations before (namely Calvinism, which I am not of that camp) but from the inverse idea that one cannot choose to believe God because only God can choose us.

This is indeed something that Calvinists believe. Calvinists agree with the rules of the game as formulated by John Calvin, a theologian, not coincidentally, trained as a lawyer who preached that only a small minority of people go to Heaven and those "elect" were chosen by God before they were born, before the beginning of time, so nothing anybody did in life could change his or her probably hellbound trajectory.

And that does have basis in the Bible because some parts of it say that humans indeed don't have free will in this and everybody is already predestined, like

Romans 8:29-30
For whom he did foreknow, he also did predestinate.... Moreover whom he did predestinate, them he also called: and whom he called, them he also justified: and whom he justified, them he also glorified.

Ephesians 1:4-5
He hath chosen us in him before the foundation of the world, that we should be holy and without blame before him in love: Having predestinated us unto the adoption of children by Jesus Christ to himself, according to the good pleasure of his will.

2 Timothy 1:9
Who hath saved us, and called us with an holy calling, not according to our works, but according to his own purpose and grace, which was given us in Christ Jesus before the world began.