A physical god, not a metaphysical one, would be subject to the laws of physics, and could therefore only exist in space-time (space plus time). Space-time is bound to the universe according to current cosmological models.
Based on our limited current knowledge, the universe will expand forever, and changes will slow down over very long timescales ("heat death").
Hence a physical god of whatever properties in detail would gradually cease to exist in the sense of being a distinguishable and active individual; that's roughly equivalent to sitting there and doing gradually less and less, and ending up in perfect randomness without goal or direction. This is not just because of possible asymptotically and locally reaching maximum entropy, but also by thinning due to exponential expansion of the universe.
At the end, there is nothing else than expanding vacuum with random fluctuations near absoute zero temperature.
Or using the "god" metaphor: A physical god is sitting there, and is bored, forever.
Outside our space-time, beyond physical infinity, other space-times may (metaphysically) exist, with other life-forms pondering about their universe and beyond.
In a many-worlds multiverse space-times can be related to each other, although without physical communication between them, in a way that one could define something like a common time for at least some of the universes. In this scenario, the existence of a god in one universe would imply an infinite number of similar, but not quite identical god-twins, at most one per parallel universe.
This could also be interpreted as an infinite sequence of infinite periods of time, infinitely many, although not necessarily all of the items of the infinite sequence, causing a rebirth of a presumed god, each one with a similar, but not necessarily identical fate.