I do believe in God, but all the same - I think I may be able to ‘steel man’ what some responses might be from atheist quarters - and a any of our friendly atheists around here can chime in about how I do, or add their own corrections / insights.
Dale may have already touched on much of this above, but at least some of the fine-tuning could be explained as adaptive response. I.e. … we are organisms that need to live within certain parameters of temperature / pressure / atmospheric composition / etc. …and so voila! It’s a good thing that this is exactly what we have! But this is like Douglas Adams’ proverbial puddle of water rejoicing that the hole in which it happens to be is just exactly the right shape for what the puddle needed! Which is silly because the puddle is formed by the depression - just as we are adapted to the environment within which we find ourselves.
Of course fine-tuning is not completely answered by that, though - there are still genuine amazements in terms of physical constants being on a hairs-breadth ‘knife-edge’ away from total non-viability for much anything (much less life). Some answer to that might be to fall back on a multiverse possibility - perhaps trillions of other universes were non-viable - and; no surprise! We would not be in any of those to be able to comment on it. In any case, even if this is the only universe - we just don’t know enough about how such constants could be “tweaked” or “selected” in the first place. Maybe there was some necessity in them (like the geometric necessity that pi must be about 3.14159) that makes them less contingent somehow. And that’s the problem here … jumping from “here is a very precisely needed value” to “therefore there must be a personal Creator God” (much less a specifically Christian one) seems an unwarranted jump to responding atheists. While they might find this interesting (even amazing), it would need to be accompanied by other independent evidence (preferably much more specific evidence).
As for saying “the fact that there is anything that exists at all - implies an initial cause” or an ‘uncaused-cause’, that too is quite non-specific evidence that such a cause must be what Judeo-Christians describe as a personal Creator God. Perhaps there is some infinite regression - maybe the big bang is one of an infinitely recurring number of cycles, etc. There is just too much that is unknown.
The moral argument is one that has been dismissed as a kind of “special pleading” that it would be highly undesirable for our moral structures to not have any objective grounding. Even if this were true, it doesn’t follow that this makes evidence for such absolute moral foundation. Our wanting it to be true (even if it is conceded that it would be very good for it to be true) nevertheless does not constitute evidence that it actually is true. Atheists have pointed out that nonbelievers find quite enough basis for their own contextualized cultural morality just in the surrounding culture alone; and they don’t all fly off the handle into nihilism just because they fail to believe there was an absolute moral-giver chiseling it all in stone.
That is what I think might sum up some atheist responses to all this. As a believer myself, I engage with all that too (and concede that they are valid - though not unanswerable points). My belief isn’t anchored in my being able to ‘refute’ all the above or give it any stunning rebuttals (I can’t). My faith is anchored on much other grounds which provides me a context to see all the above. And so long as my faith context remains plausible (not asking of me that I accept demonstrably false things as true), then I remain undisturbed by my inability to address all such physical mystery.