The above quote from Rabbi Miller is an example of a version of the fine tuning argument.
Even if you would accept the fine tuning argument at best its utility is against the position of randomness. What’s the next step? Most world religions would accept this argument as would the classic philosophers yet their conception of G-D is certainly false.
When (most people) ask for proof of the existence of G-D what they really mean is proof of The G-D who gave US laws, runs (present tense) OUR world, hears OUR prayers.
It is Yitzias Mitzraim and the Revelation at Sinai that is the only rational evidence of revelation. And it is through revelation that we know everything else. Post revelation a study of our unique history as the chosen recipients of the Torah is also relevant evidence.
@ DovidBT
“An atheist could argue that everything in the above post can be explained by science”
1) What someone “can argue” is not relevant. Ever. A “could argue” without positive evidence is a very weak position and not worthy of a response.
2) Explaining the mechanism by which natural events occur is not an argument against the existence of G-D. It is a straw man argument built on the false premise that believers have no positive evidence for the existence of G-D and use Him to explain what is (was) to them otherwise inexplicable phenomena.
It is also worth pointing out that essentially Emuna is the natural experience we are endowed with by our Creator. Rational argumentation is a tool we use against the the olam hagashmi, the yetzer ha-ra, the culture of the umos haolam, and our own sins which obstruct / corrupt this experience. See Kuzari shar aleph. Also see HaRav Aaron Feldmans excellent article in the latest issue of Dialogue.