I think you are still unclear on the concept. Here's an analogy: A scientist hypothesizes that a new particle, particle X exists. Why does he do this? Perhaps it just seems to make sense from beauty of nature / symmetry argument. Suppose if X exists, it simplifies some existing math or makes sense of some existing known aspect of reality in an elegant way. The only problem is there's not one shred of evidence for X. Is this a bad thing? Not necessarily. Perhaps his X particle can be shown to predict some new result that we don't currently have an ability to measure... but we might someday. Well then, we put his X hypothesis on the shelf until that day arrives (if it ever does). In fact, maybe there's so much interest in this X hypothesis that it can be used to justify some spending to build a new sensor to see if the predictions based on X existing are true. Nothing wrong with any of that.
But we don't go around insisting that X exists UNTIL we start seeing some tests passed! We make sure those predictions come true. And if we come up with new predictions (new ways to test the X hypothesis) we also test those. This is a potentially never ending process... we keep coming up with new ways to test X and we keep testing for it. Until, we one day discover a test that the X hypothesis fails, and it's time to move on to a Y-hypothesis, which explains all the previous results, PLUS the new results that the X hypothesis cannot explain. Make sense? Will the Y-hypothesis definitely replace the X one some day? No, not necessarily. Perhaps the X hypothesis will continue to pass every test we throw at it forever.
The point is, we don't go believing in X until we have lots of good evidence for it. What if X sits on the shelf, untestable due to technological constraints for centuries. Well then, it sits there and we can't really say it's true. We have to assume the null hypothesis (i.e. reject the claim that X exists) until such time as there's at least a shred of evidence to support X.
Same goes for the God hypothesis. The trouble is that most God hypotheses are not even testable in a scientific sense, nor will they ever be testable. Occam's razor says such hypotheses are useless and should be eliminated from consideration. But just for the sake of argument, say somebody comes up with a God hypothesis that could conceivably be tested one day. OK, great, we'll just have to wait until that day arrives then.
There's no proving the God hypothesis nor disproving it until we can test it. And even if we do disprove it, it does not necessarily preclude a different God hypothesis from being proposed. Even if the hypothesis was untestable by design and discarded by Occam's razor, then that still doesn't mean it was disproved: it just means that it was useless (i.e. untestable forever).
So to say "atheists are correct" is a weird statement. An atheist is not necessarily claiming anything! In particular it's not necessary for the atheist to be claiming that god does not exist. In fact the atheist could reject the claim that god does not exist for the same reason he rejects the claim that god exists: lack of evidence. "Rejecting the claim" could mean simply withholding judgement on the claim. It does NOT mean supporting the opposite claim.
Anything different than believing gods exist, is atheism, by definition. For example that could be:
1. Withholding judgement on the claim that gods exist. This could go hand in hand with withholding judgement on the claim that gods definitely don't exist.
2. Believing (based on the preponderance of evidence, or for any other reason) that gods don't exit, but not claiming to know for certain that they don't exist.
3. Claiming to KNOW for certain that gods don't exist
All three are different "degrees" of atheism. Both 1. and 2. fall under the category of "agnostic atheism" because they are not claiming to know (a gnostic claim) that gods don't exist. See my source for more info.
EDIT: In response to "Redeemed" above, note the difference between what I've laid out above and what he's talking about. What he's describing is a logical proof, more akin to finding a proof of the truth or falsehood of Fermat's Last Theorem (which bedeviled mathematicians for centuries until it was finally proved to be true in the 1990s). Mathematics is very unlike science in that regard. With math you assume some things are true to start out with (axioms) and as long as the axioms are not contradictory, you can proceed to deduce logical consequences from them. That's not really how science works. Science starts with a guess (hypothesis) and then the guess is checked against nature. What's missing from Redeemed's argument is any checking against nature. He's only talking about proofs, but what are the axioms they rest on? If you start off with an axiom that buries within it an assumption of what you're trying to prove, that's called "assuming the conclusion" and is a fallacy. For example, I could start off with "What caused creation?" and end up with "A creator must exist." But by using the word "creator" in the question, I'm assuming already a creator must exist. Be careful of rationality unmoored from empirical testing against nature!