Cause and effect arguments for a God simply end with special pleading in the case of God. Not just God himself but the space/dimension it which that God exists. Which came first the space/dimension in which God exists or God?
To say that God can’t exist because he would need to have a cause or exist in space or time is really no different than saying that “God can’t exist because God can’t exist”. It’s not an argument it’s an assertion.
God is outside time and space by definition. The point of God is that he doesn’t have a location in space or time and is self-caused. As Aquinas pointed out, causes either proceed in an infinite series or else there is an ultimate cause. Reflection (which is what the five ways call for) leads many, including myself, to conclude that an ultimate cause makes intuitive sense. It’s not a deductive or an inductive argument, but it seems like the best explanation.