I believe only in logic. And I haven’t heard of Godel “proof for God existence” nor his “proof for the non-existence of time”.
But in either case, I can already deduce that either he was entirely incorrect, or is merely being reported fallaciously (as often occurs regarding Science issues).
I think that you’re asking science to respond to philosophical questions. You remember when you were like 5 years old in elementary school and the teacher told you, “correlation isn’t causation”? At the time no one knew what that meant because we were all 5 years old or something. Now we get it so we don’t ask why science can’t answer the problem of first cause.
A parallel universe? That sounds like poorly defined hokey kind of term that doesn’t really mean anything. Like totally ripe for equivocation. I’d avoid it.
The closest thing I can think of in philosophy would be possible worlds. In the case of those, like many things in philosophy it doesn’t come down to whether or not one can demonstrate them observably but instead whether or not they can be refuted. I think there’s some pretty tricky arguments for possible worlds that are very hard to understand, and even harder to refute. Most people fail to understand them and then assume they’ve refuted their own strawman version. It’s all good.
It is modern science which claims that it can answer philosophical questions. I too agree that it cannot.
Science is based on specific axioms. These axioms are generated by philosophy. And you cannot question your foundations so easily.
However the existence of a “First Cause” can be explored through Logic. Cause and effect are notions which can be explored in theoretical level even if you do not have immediate experience of them.