This is somewhat puzzling. The Bible indicates that God fills all space, is ever present and created us in His image. If this is true, how (and why) would He be totally apart from us? And how could we (the image) be so different from our Source?
"Free will" is not the answer because God must have free will and God does not choose evil - if man is His image, man would not choose evil either.
His creation is material. He is Spirit. That sets Him apart from us.
He states point-blank that all have sinned and come short of the Glory of God, and that our sin has separated us from God. That, too, sets us apart.
The fact that we are in His image and likeness probably refers to the fact that we, too, are spiritual beings, individual, willful and able to "create" -- but these characteristics in us are measured, finite. Not so with God, who has all without limit or measure.
So, if you're right and I'm wrong, what's the upshot? My sin is that I'm God and didn't know it? On the other hand...