The basic problem with the non-theists or atheists is that they assume
if they know what exactly should be a God if it exists but they donot even
understand and know the exact definition of God.

If any person brings me a pencil and tries to prove me that it is a pen offcourse I'll reject him and prove him wrong because I know what a pen is and how it looks like.
Now for example If I donot even believe in the existance of pen and keep on criticising the person who tries to prove a pencil as a pen then it is a blind criticism and nothing else.
A person who does not believe in a pen will always deny a person whether the person is trying to prove a pencil as a pen or a pen as a pen.
Similarly an atheist who doesnot even believe in God and doesnot even know the definition of God will always reject any concept of God.

Another problem is that different religious sources have different concept of God and when an atheist comes across such concepts he or she becomes confused.

The point I am making is that unless and until a true concept of God is
explained to an atheist, its no use.

No, not really. If a being inspires awe or teaches us how to advance in our lives, the reality of what that being actually is becomes a moot point.

And I've never figured out how humans would go about verifying a god's credentials, anyway. It's not as if we can follow a god-like being around the universe or determine that there isn't an even higher entity... Perhaps a god doesn't even know that for sure.

We live on a small particle in a molecule in a cell of God.
As above, so below.
Time then would be relative to your size and your awareness.
There are other higher beings than us which we would qualify as being gods as they are more advanced than us.
They live longer than us and are not afflicted with the same weaknesses.
They have greater "powers" which are obvious and easily verifiable.
So we would think of them as gods which just means higher beings or higher in the hierarchy of LIFE, but they are not GOD, they function in tandem with GOD (or sometimes not as there are cycles of chaos and order which occur).
Some of these beings have chosen to "rebel" and so are not in harmony with order, they serve their self.
So it is impossible to know what the GOD looks like as there is nothing in creation which is the same as the big picture GOD, but there are a lot of resemblances due to the fact that there is a pattern.

the only Human text of human investigation upon your question that has stood the stand of time untold.
with out dissbute.

That which makes a God Is that which Does not Make a God.
That Which is devoid of ATTACHMENT is God.
Listen to me now hear me later?/
Godhood/ God head is the mind of detached desire to know god. And God IS.

What makes a God?
perhaps a childs imagination?
without a doubt the greatest of attributes of god is elloquence or so my religions' has' told.

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GOD is an Acronym, G:reatest O:mnipotent D:eity