It's a little unusual (to my ear), but you can use
get that way. It suggests a gradual process that terminated in the full realization. This way of casting the thought would go well with an introductory phrase like
After much thought.
I suspect there are very few verbs that can go after got to with this meaning. realize seems to be one of them. Perhaps other verbs of mental accomplishment can also be used.
After years of experience, the teacher got to know how to present that concept effectively to beginners.
Peter eventually got to understand that his parents really had his best interests at heart. They were not simply mean people.
A good substitution is came instead of got. I think I prefer came in these cases.
Sam came to realize ...
The teacher came to know how ...
Peter eventually came to understand ...
CJ