This depends on the life of the one making the decision. If the person has seen that life is falling apart for himself, and if he has tried all kinds of things to change it, he might decide to suddenly believe because he has (or thinks he has) tried everything else. However, this might not be the way for everyone.

Some people are reasonably honest, thinking people. They say to themselves, "Smart people build all kinds of complex technology, yet the universe defies their understanding because it is so extremely complex. Where does that great complexity come from? Well, let's see. Man-made complexity comes from intelligence of people. So, universe complexity must come from something even more intelligent. I don't know if the man in the sky is really a man, and I don't know if he/it is even human, but he/it is extremely intelligent to have built complexity that man can't figure out."

So, it is not necessarily a sudden belief, nor is it necessarily a sudden decision. It is simply a direction of thinking.

In addition, if the person happens to check out the Bible at this stage of the game, the Holy Spirit works in the person's heart to come to understand God enough to believe in Him.