I think the question you're really asking is whether or not I can know something without a propositional understanding of it. "God exists" is a propositional statement. There is knowledge that goes beyond what can be put forth in propositional terms. For instance, I might say many things about knowing my wife but even if I exhaust every logical proposition to describe what that means there is more to my knowledge of my wife than what I can express propositionally.
The unbeliever knows God exists but not in a way that He will express in a propositional way. He will assume the regularity of things and the reality of his existence. Both of these things witness to a knowledge of a Creator even as he suppresses the requirement that he worship God for these facts.
I think the question you're really asking is whether or not I can know something without a propositional understanding of it. "God exists" is a propositional statement. There is knowledge that goes beyond what can be put forth in propositional terms. For instance, I might say many things about knowing my wife but even if I exhaust every logical proposition to describe what that means there is more to my knowledge of my wife than what I can express propositionally.
The unbeliever knows God exists but not in a way that He will express in a propositional way. He will assume the regularity of things and the reality of his existence. Both of these things witness to a knowledge of a Creator even as he suppresses the requirement that he worship God for these facts.
People know the laws of logic, morality and nature and are, often, not conscious of them.
"Presuppositionalist" apologists point out this knowledge as evidence of our knowledge of the true God, even in those of us men who deny that God exists.
It was Enlightenment philosophes, like Rousseau, who said that Man was a tabula rasa, without any innate knowledge at birth.
I think there needs to be a distinction in knowledge that one CAN become aware of propositionally and knowledge that one could NEVER put into words. I believe there is such a knowledge that cannot ever be put into words, a kind of knowledge that is not supposed to be verbal. Not to stir up a hornet's nest here, but Scripture speaks of the Spirit's groanings which are too deep for words. We have all encountered things of beauty that we could not put into words. I'm sure there are others too.