edit - Title should read: How can you claim to know the unknowable -or- How can you claim to have knowledge of the unknowable.

I'm an agnostic atheist, and I can't wrap my head around the belief of a gnostic atheist.

Even though I don't agree, I can understand that if a theist has a belief in god, they can have gnostic or agnostic beliefs about knowledge. If god exists, this could be knowable by god showing us his existence. If he doesn't do this, then this knowledge may or may not be knowable.

I can't comprehend how someone who doesn't believe in god(s) can claim to know, with all certainty, that knowledge of a supreme being is attainable and thus either verifiable or falsifiable.

TL;DR - Please explain how/why you think we can know that god doesn't exist.

EDIT

There are a lot of good points made here. I think I must concede that my ideas about absolute knowledge are too strict. From a completely existential stand-point, I suppose there really isn't anything that I know for absolute certainty. After all, the probability that everything is just a figment of my imagination (and I'm just a brain in a vat) is not zero, but I still know this isn't true.

For most definitions of God, I've always been agnostic atheist. The reason I've never classified my beliefs as gnostic atheist is because of the small probability that something supernatural exists outside our realm of understanding. I think after reading all the arguments here, this seems to be the case of most people who classify themselves as gnostic atheist. The main problem I had before was the definition of knowledge. From now on, the definition of knowledge I will be using is "beyond all reasonable doubt", and under that definition, I've definitely seen enough evidence in my life to be gnostic atheist.

Thanks to all for helping me better understand! I love this subreddit :)