Ok, back to something meaningful....
Well, many modern conceptions of the Christian God only have him operating in areas that modern science doesn't really understand well, like influencing people's thoughts and feelings and only operating in other areas when no one is looking. That would seem to fit the definition of a god that theoretically ought to be detectable, but is currently outside our abilities. As the workings of the human brain are further explored, this could change. Until scientific knowledge is complete, we can always ascribe God powers that only operate in whatever area we don't understand.
Actually, the basics of "influencing people's thoughts and feelings" is well enough understood to make some meaningful observations which are fatal to God-theory.
Our thoughts and emotions arise from the activity of the brain, and the extended nervous system. This model has been empirically verified through every means devised to test it. There is no other competing model.
Therefore, our thoughts and feelings always have a material/energetic state associated with them.
In order to influence this material/energetic state, there must be an input (e.g., light hitting my eyes, sound waves striking my ear, chemicals entering my digestive system or blood).
For God to have the ability to influence our thoughts and feelings, it would have to interact with us, to expend energy. Which means that God would have to be local (though not necessarily exclusively local), and at least possess potential energy in some form.
This presents 2 basic problems.
First, we now have terrestrial instruments sensitive enough to detect the CMB. Yet we have not detected anything beyond the known stuff of earthly life and matter which would possess the potential energy to influence our thoughts and feelings.
And if God has this potential energy locally, then because E=MC^2, we must conclude that it would be possible to convert some of God's energy into matter, so you could have a half gram of God in an urn on your bookcase. Yet this idea is repugnant to mainstream notions of God.
As for the proposals that (1) we can't currently detect God, or (2) we can't deny God until we know everything about everything....
The first proposal only becomes relevant when we have some definite notion of what we're talking about. Otherwise, we're left asking "can't currently detect
what?"
The second proposal is simply untrue. Entities are defined by their qualities. Once we know these qualities, we only need to know enough to consider them. I cannot imagine (and have never seen proposed) a quality which would require omniscience to consider.