I think (not "I know" or "I believe") that a part of God being infinite is that God is transfinite.
Let me explain and define my terms. If we were all points on a plane (a flat, two dimensional world), a solid sphere that intersected the sphere would be a transfinite object (vis a vis the plane).
Just as the number of curves in the plane is infinite (an aleph two infinity), so the number of curved planar surfaces inside a sphere is infinite (and perhaps sufficient to correlate to the curves).
I think that, in some ways, the resurrection makes us transfinite. The sort of thing C. S. Lewis grasped at with his book The Great Divorce. Lewis has things getting more and more real as they get closer to God (all of hell is contained in a speck at the bottom of a crack in the pavement at the edge of Heaven). I suspect that all of our grasping at meaning is limited by our lack of a transfinite nature and by our finite understandings. Which is why John would say that it does not yet appear what we shall be. ("Beloved, it does not yet appear what we shall be, but we know that, when he comes, we shall be like him.” So love for one another, genuine love")
He knew we would be resurrected and become like Christ, yet his best analysis of that was that we should embrace love, because he could not otherwise define it.
So it is that I don't really know or really define, but it appears to me that much of the infinite may be subsumed in the transfinite.
By the way, I listened, a while back, to some of the people whose stories are told in "God Grew Tired of Us." The movie is out now. I think I need to see it.