The fine-tuning argument for God’s existence is a very popular argument these days. One of the problems with the argument that is often overlooked is what I will call the “gap problem” or problem of alternative explanations.
Roughly speaking, even if we grant that design best accounts for the fine-tuning problem, it’s not clear that theism is the best explanation. And, even if theism was the best explanation, it’s not clear why the God of classical theism would be the best candidate, as opposed to some other supernatural explanation or theistic explanation. In terms of theistic explanations, fine-tuning can be accounted for by an evil god, an indifferent god, a god that is quasi-maximally great, etc.
Granting that fine-tuning is due to design, it’s not clear that we can easily rule out naturalistic explanations. For instance, what if there are aliens or superhumans who designed the universe? What if we are in a simulation? Someone might object that these explanations are implausible. But the question is whether they are more or less (or equally) plausible as the theistic hypothesis.