I remember your asking who/what God is, and I remember my replying with "God is Spirit...", but I missed your follow-on question. It's a natural response to my answer, so I'm sorry I missed it.
I think nature itself teaches that God is not of this dimension. Spirit is the word for the God-dimension.
How do I know that it intersects this dimension? There are many answers to include prophecy, divine intervention, biblical record, etc., but one of the interesting ones I ran across about a decade ago was a bit of research in which folks had been asked if they'd experienced an unusual event that they could only explain as God. It was a huge percent. I'm going to have to look it up again. I used it in a program I presented at Kansas State entitled "The Spiritual Dimension of Family Living." I've probably got it lying around in some dusty file box someplace.
Oh, I hope you will find it xzins! It would be interesting to "compare notes" on experiences of such "unusual events." I've had a few such "unusual events" myself....