I don’t find the fine tuning argument convincing for the following reasons:
If you change constants in the equations that govern the laws of nature, even slightly, it is true that the Universe will change a lot. However, there is no justification for the claim that life in this new Universe couldn’t exist. This is because nobody yet knows the full range of conditions under which life can exist.
The whole argument implies that God is somehow restricted in the sense that if he wanted to create life like ours in a Universe, then the range of constants that he could choose from was limited to a narrow range. Being omnipotent, God could create life in any Universe, no matter what the laws of nature in that Universe are.
We can’t say anything about the likelihood of a Universe such as ours (with our physical constants) coming into existence, because we only have a sample of size one. This is analogous to taking out a red ball from a bag of different colored balls (colors and numbers unknown) and then trying to estimate the likelihood of drawing a red ball.
It is possible that an infinite number of universes may be popping into existence within some larger Multiverse, with each Universe having random physical laws and constants. If this is true, one would eventually get a Universe with our laws and constants by pure chance.
I’d love to hear what others think about the above.