we're all familiar with Popper's dictum that if a theory, a claim explains everything, if everything is consistent with the truth of the claim, then it's empty. It doesn't explain anything at all.
[On the claim that Science purports to explain everything, or that it claims that it will be able to eventually] I don't think Science does claim that at all, in fact. Science at its normal best: it is a public, a testable, a challengeable project. Always having to maintain its own respectability by saying what would count as counter-evidence against it.
And when people put forward views in Science, they publish them so that other people can test them, review them, try to replicate results, and I think that is absolutely the model of how an epistemology should proceed. Out there in the open and inviting the very toughest kind of response from other people...