I think you mean no such thing as proving a negative.
Yes, there is such a thing.
I think you missed half my point. I asset there's no way to prove or disprove a god using current scientific methods because "god" is not a properly scientifically defined concept, and will never be, and speaking of proofs/"disproofs"/scientific reason etc with respect to god is useless.
Surely it's possible to disprove god if you put some effort into it. The problem is that you have to go into uncharted territory, because there's no point in disproving something's existence. The way how science works, the scientific method, avoids all such nonsense altogether by investing how the universe does work and what does exist, and not how it doesn't or what doesn't.
However, it's easily enough possible to extend the principles of science (the scientific method) beyond where it's used in practice to come up with an explanation of god's nonexistence that's as scientific (as accurate) as realistically possible.
Also, I'd disagree with your assertion that god is not well defined. God is simply a supernatural being (it doesn't obey the laws of nature). As long as there is not even evidence of something supernatural, than surely there's not evidence of god's existence as well, which works more than good enough when trying to disprove god (because assuming that everything that's supernatural is god actually makes the chance of proving god higher).
Sure, believers would like to someday prove god with the scientific method but IMO it's a pipe dream. Better to drop that altogether and be honest with yourself, that you're believing something that can't be proven currently with our science.
To elaborate on what I said above; disproving of course depends on your definition. How rigorous do you want to be? To me the certainty is more than high enough, so searching for evidence seems an exercise in futility, because the chance that you'll find evidence is simply too low. This isn't a deficiency of the scientific method, it simply means that god doesn't exist.
To give an interesting example of why it isn't interesting to search for low probability explanations: life.
What science basically tries to do is find the easiest, simplest explanations of things (but not simpler, as Einstein said), so it should be obvious that biologists are wasting their time if earth really is the only planet with life; they'd have to search for an
improbable explanation for how life could arise from nothing, which of course contradicts the principle I just explained.
However, we can disprove it with current scientific methods. There's no scientific way to measure souls with our current knowledge (scientists have tried weight bodies before/after death). Without this, we can conclude with our current knowledge that such a thing doesn't happen.
Sure, in the future we might find a cause for this, but that's really speculation.
But why do we actually have the concept of soul in the first place? Because ancient people invented it because they were afraid of death. So why should it be tested against reality if there isn't even a scientific need for such a concept at all?
My general rule of thumb is that most assumptions people have are wrong. This is exactly why.
So you'll have to take it as a belief without evidence. Which is fine, but don't bring the scientific method into this.
No, people must bring the scientific method into it, because it should make them realize that god in all likeliness does not exist or at least that their ideas don't have a reliable origin (an origin that isn't science).