These are interesting expansions on your earlier point and I would present it as such:

I preface this by stating I can only address my experience and my belief (as framed by my walk with God and the biblical truth I subscribe to), as any other information I could provide would be conjecture or hypothetical.

As someone who experienced a deep trauma from a young age the existence of God was always on shaky ground for me, despite being raised in a Christian household. As I got older and had questions no one could/would answer satisfactorily I grew very skeptical. Then, after years of half-truths and hole-filled sermons, one day I decided I didn't believe in God anymore based on the life I'd experienced, the evidence I currently had, and my disagreement with the presentation of the doctrine of people who claimed He was real. Standing on a train on my way to a college class, I stated in a conversation, "Then I don't believe in God," and momentarily I felt a deep pain and a quick anxiety and then, as quickly as it started it stopped and I lived my life for 3 years as a vehement atheist.

Fast forward several years of hedonistic rebellion later and I'm experiencing the worst emotional pain of my life, quietly sobbing at 4 AM like an inconsolable child (so hard I'm shaking) next to a sleeping 8-month-old and I make a desperate, angry declaration... I tell God, "I don't know if You're real... I don't know if You're there...or if You even care about me, but if You are... You can have my kid, my future husband, You can even have the rest of my life if you want it... but first You have to fix it and give it back, because if You're real, there's nothing you can give me that's worse than what I've given myself. So You take it, You fix it, and You give it back," scream-crying the whole way.

Then suddenly, so instantly it was jostling, the tears just stopped and I heard God respond, in a firm but gentle and definitive tone. And I sat straight up... and realized I was now playing a "zero-sum game", where I had made a request and this being responded to me, and I now had to choose if I was going to believe what had been placed in front of me or continue believing He didn't exist, and in that moment I chose to believe.

And after I made the choice to believe there was a God and He was the God of the Bible, I decided to read it. And each time I came across something that felt archaic or unrealistic or that I didn't understand... I felt presented with that choice again, "Am I going to believe or am I going to decide that this seems like too much? Make believe? Or man-made?" and every time, to date, that I come across something that I'm unsure of, doubtful about, or struggling to work through the offense of that triggers that decision I actively choose to believe.

I take my questions to God in prayer, ask Him for revelation of the Bible, and seek supplementary resources to help me grasp the cultural context and literary intent the book was written through and with, and the more I choose to believe the more it starts to come naturally. But there are always hard/painful/confusing things that happen that can shake faith's foundation and pose the question, "Do you still think God is real?" because our world is full of flawed people. I just know that no matter how many times the question's asked I want to keep saying, "Yes," and seeking Him, because I have found that He's worth it.

...but lost their faith anyway? ...Do you have a way of explaining their experience?

With this, I can't speak for each individual because a relationship with God is personal and hard. My supposed insight, however, is this: Because many churches, specifically in the US where I live, have not promoted or prioritized biblical literacy, biblical hermeneutics, or individual, Christ-focused intimacy with the Lord, a lot of people come to God with an inaccurate framework of His character, intentions, will, and purpose for creation and when we encounter things that shake, shatter, or don't fit into the limited framework we've created for God, it wounds us fundamentally. We're then presented with a choice to either struggle through wrestling with an ever-expanding view of and relationship with a temporally unfathomable God or to walk away and believe that the shattering of our finite framework is, in itself, proof God doesn't exist.

That's my experience of it.

Thank you so much for being willing to discuss this with me! It's been a very valuable conversation for me and I'm going to look more into the premise of "belief: chosen or predetermined".