I’ve always assumed that I’m justified in stating that there is a non-zero probability that creator god exists. I assume this justification due to the limits of my knowledge, although I imagine the probability to be approaching zero - say 1 * 10-googolplex on any average partly cloudy Tuesday.
Here’s where creator god becomes untenable: in order to put him (her, it, etc) in a position capable of creating the universe, it's usually claimed to be (quoting Dr. Wm. Lane Craig) “beginningless, changeless, immaterial, timeless, spaceless, and enormously powerful and intelligent“ - thus creator god must be understood to have an existence separate from this universe. That’s the key: creator god must first exist. So creator god does not create existence. Therefore creator god is not the greatest imaginable being - only a being capable of creating “creator god world” is. But then who created the creator of “creator god world” ... and so on? This has always been the criticism of assertions like “God created the universe” - they reduce to infinite regress, and require defending via special pleading or bare assertion. Illogical!