What exactly is the argument here from fine-tuning to the existence of God? If one of the premises is “we could have lived in a universe that does not support life,” then it’s clearly false. In a non-life supporting universe we would not exist.
This perversion can be escaped if we postulate an angel somewhere in the high heavens observing our universe and wondering why it exists.
Now in my book I use a simple argument in favor of God’s existence as follows:
… the problem of particularity: why is the world this and not something else? Either it was designed for a purpose, such that the purpose (or end) constrained the universe (or means) to a single thing or at least a finite set; or its essence was randomly pulled somehow out of an infinity of possible worlds. But not the latter, because the probability of this world’s being chosen in such a way is exactly zero. It is impossible to consider for selection every member of an infinite set. So, it was designed. But purposive design entails choosing between possibilities and suggests an intelligence at work behind the scenes. Hence, another conclusion: God is smart. (I, 29)
The fine-tuning argument can work only if the total number of life-supporting possible worlds is finite. Then the problem of particularity will be felt pointedly. If it is rather infinite, then the probability of its coming to exist randomly cannot be evaluated, and the argument fails.
Unless one is willing to go so far as to assert that “any world that would not at some point support intelligent life cannot for such-and-such reasons possibly exist.”