I maintain the position that we cannot disprove ‘god’ as a generic idea, but usually because the concept is not defined sufficiently. When it comes to specific proposed concepts of god, we can (and have) disprove the proposition by use of scientific and/or logical analysis. Basically, the more clearly a person defines a god, the easier it is to disprove its existence. The more vague, the harder it is to do so.
Of course, at the same time, the more vague a definition proposed, the less powerful and useful the god. The “eternal ground of being” of Paul Tillich and many of his liberal theologian followers have a concept of god that is impotent, and not the god described in the Bible, Koran, etc. One could call their teapot god, and I would be compelled to agree that this thing exists if presented (empirical evidence), but I am not compelled to consider it’s powers sufficient to call it ‘god’.
When pushed, many theists will resort to a god not unlike this teapot in power, except even then they cannot demonstrate its existence, but rather define it such that its existence is beyond our ability to test, at least until neural scanning improves considerably.
‘God’, in most cases, is an incomprehensible being, whether due to logical incoherence or semantic conflation.
I believe the most epistemologically sound position is something like this; the lack of evidence for supernatural beings, in conjunction with the logical incoherence of major concepts of deities, leads us to conclude that belief in concepts such as gods are unjustified. Science can indeed disprove many concepts of god, but the rest will be left to the dustbin of impotence or uselessness. There is no room in this universe for a sufficiently strong deity that exists, in order to call it ‘god’.