This is the doctrine as I know it. Yes, while God is omnipotent and could break that rule, he doesn’t. Why? There are two main traits that define god, loving and just. He loves us enough to send himself to save us and provide a way, even though we do absolutely nothing to deserve it.

However, because he is just he allows us to make a choice. For if there is no choice, there really isn’t a relationship at all, he gives us the choice to choose him or live life on our own.

As far as situations where people aren’t given a chance to choose this forgiveness, it enters a gray area and I don’t know enough about it to be comfortable sharing