As soon as you can distinguish your concept from a description of something that doesn't exist, there's necessarily some testable description that we can compare against what we have observed of reality.
Yes. So what is a god?
The most common definitions are:
1) A being that influences the lives of humans, determining who is successful and who is not
2) A being that can be lobbied to intervene in the lives of humans (as in 1, above) by acts of prayer
3) A being that manages the continuing existence of humans after the death of their physical bodies. Lobbying for the benefit of deceased relatives and friends may be possible (as in 2, above); This lobbying may or may not be offset by punishment or reward for things done while alive
4) A being that designed and/or created and/or sustains all of the reality we observe (and possibly some that we don't, such as the afterlife conditions applicable to 3, above)
5) A being that designed and/or created and/or sustains a small fraction of the reality we observe, and that intervenes to the benefit or detriment of people who interact with that small fraction of reality (eg local gods of specific locations such as springs, mountains, lakes, rivers, etc.; Gods of larger phenomena such as the oceans and seas, the weather, fire, etc.; And gods of specific activities such as patron gods of fishermen, smiths, gamblers, etc.)
In all of the above cases, the being is distinguishable from a natural phenomenon by the ability to exert its own will to influence something, so that that thing sometimes acts in a way that couldn't have been predicted solely by the application of universal physical principles.
I think that gods fitting these descriptions cover the claims of the vast majority of religions and of religious believers; And are demonstrably impossible. However this list is just thrown together off the top of my head, so if you think I have missed something important or widely believed, I would be grateful if you would let me know.
ETA: Reviewing my post, I wonder whether all of the above could be simply summarised by saying "a non-biological guiding intelligence".