I have always found fine-tuning arguments to be a sort of argument from ignorance, in that they tend to ignore the possibility of other forms of intelligence. While they might be correct in claiming that if the physical constants were significantly different then our form of carbon-based organic life could not arise, they don’t really succeed in excluding other possibilities.
Sometimes I imagine that there could be universes with intelligent life that imagine that it’s their own universe that’s fine-tuned, and them unable to imagine life emerging in a universe that is almost entirely empty like our own. (Greg Egan’s Schild’s Ladder deals with similar concepts.) Or perhaps galaxy-wide life forms that somehow emerge from the interactions of entire stars acting similarly to cells might be unable to conceive of intelligence at an incredibly microscopic and fast scale like us. Thoughts like these sometimes makes me wonder whether we could even recognize some forms sentience even when it’s in plain sight.
Stephen Baxter has a good grasp on how fragile the fine-tuning argument is, and he draws a vivid picture of what alternative forms of life could have arisen throughout the development of the universe in his Xeelee Sequence of stories, from those that form from defects in space-time itself to carbon-based life forms like ourselves. And really, given only the fundamental laws of physics we know today, could anyone have predicted the rise of carbon-based intelligent life like humans? Just because we don’t know how intelligence could arise from different laws of physics doesn’t mean it’s impossible.