I agree. We can't know if there isn't, but we CAN know if there is. As you say, if we agree on the idea/qualities of what a "God" is, and we find definitive proof of its/his/hers (I know know God's preferred pronoun) existence, then we can know.
I'd modify that for all sides. Don't mean to get turdy with semantics, but "proof" is only possible in mathematics and is an unreasonable standard. I like to go with sufficient evidence, or strong evidence, or whatever you'd like to call it. There's always some ad hoc explanation that jumps through whatever hoops necessary that can't be falsified, but which is logically possible, and precludes "proof" of something.
What I think is important is for positions to meet some scientific standards, so to speak. The philosophy of science, not the measuring-in-a-test-tube practice of science, I mean. Something either needs to be falsifiable, or it should meet the criteria for inference-to-best-explanation. Preferably both. Otherwise, we're just arbitrarily asserting whatever we want to be true.
The principle of falsifiability is something I think is overlooked, and shouldn't be. If we're going to have a serious worldview on something like this, or anything, there needs to be some standard by which we could be shown to be wrong. But I don't think the average person has ever thought about what their criteria for falsifiability would be.
So for example, when you say "We can't know if there's a God," then by what metric(s) could you be shown to be wrong? If an atheist says "There's no God," same thing, what conditions need to be met in order to show that's wrong? If a theist says "There is a God," same thing again. If it's not falsifiable, then I don't consider it a strong or worthwhile stance.
And again, I think "proof" is overly burdensome and not realistic. All that's needed is a reasonable standard of evidence and a paradigm of falsifiability that can plausibly be shown is avoided, and I think you've got a reasonable position.