Please don't give up chakka.
The thing is, in our world and experience, of cause and effect, there can be no room for God or so it seems, because, ad infinitum as you say, TC becomes TCTC and so on.
But, the belief in God is simply a belief in an eternal being who is His own cause and effect, complete perfection, and totally self sustaining. What we know about him cannot be by discovery via the scientific method, but only what He chooses to reveal about Himself.
To be otherwise, He would not be God.
It has been said, (J.I.Packer I think), that, "God," is the most loaded word in the English language, and I agree with this. Simply because without His revelation, He is unknowable.
God, as creator, has not made little upstart creations imbued with the power to go delving where He does not want them. Hence, revelation.
In that respect, TCTCTCTC etc etc does not come into it.