There’s a lot of baggage around what it means to say God exists. Such as all the religious dogma, and accounts of people saying God has spoken to them directly and that different regions around the world have their own versions of all this.
So I think we need to tease out the essence, or common denominator of what people mean when they say God exists.
I think we can boil God down to two attributes which can allow the argument to be developed.
1, God is the origin of us/our world.
2, God plays a role, or is involved somehow in our world.
Now if Foo was the origin of our world, and played a role in the world, then Foo would be a good candidate for being God.
But if Foo was a cute furry animal found in the world, then it wouldn’t.
Now I can’t say, if God were cute, furry, an animal and found in the world, that it would be Foo and not God. Because God by virtue of being the origin of our world is a precursor to our world and therefore can’t be found in the world. Although due to point 2, God could play a role with Foo in the world, but would not be Foo and not the origin of the world. Or in other words if God were an furry animal, God would also be the origin of the world aswell.
This is a common line of argument. There could be infinite other ineffable things out there, so why is focus in on this one, God. Well, this is because God, while being ineffable is also the origin of and deeply involved in our world. So one could say that God is the set of all ineffable things that are the origin and play an important role in the world.
We have to be able to conceive of something involved in the world, but at the same time ineffable. Because this is what most believers in Gods hold to be the case.