It made me wonder if the prospect of an infinite universe has any bearing on the probability that there exists something that would meet our standard definition of a god.
If our 'standard definition' includes creating the entire universe, being everywhere at once, and knowing everything that is or will be, then an infinite Universe makes God
less likely.
If the Universe was small enough to fit in a shoebox then being God wouldn't be that hard. Even if the Universe is a trillion times bigger than what we are aware of, there is still a slim chance that some entity could be powerful enough to create and control it. But you are positing a universe which is
infinitely large. No matter how big your 'God' is, He can't be bigger than Infinity, so to fill this universe He would have to spread Himself out infinitely thinly. And to be totally omniscient He must have infinite knowledge of this universe
plus a bit more to know Himself!
just about everything that can exist does exist
Parallel lines may continue to infinity in both directions, but no matter how far they go they cannot get any closer or further apart. If you measure the distance between a small section of two 'parallel' lines and find that it varies then you know that - infinite or not - they are not truly parallel. An omnipresent God is everywhere by definition. But if we find that He does not exist
here then we already know that He cannot exist, so there's no point looking elsewhere.
The Universe may be infinitely large, but that only makes it worse for God. Even if we found 'God' in every place we looked, there are still an infinite number places that He might
not be (and therefore is not truly God). In an infinite universe you cannot prove that God exists!