I'm not qualified to opine on the non-scientific aspects of how life began. I certainly don't agree that every random combination of atoms must be considered when assessing the probability of life coming into existence.
Carbon is not equally likely to be involved in biochemistry as uranium. The covalent bonding of carbon and the benzene ring structure are going to contribute to the formation of organic materials no matter where in the universe the carbon is found. Uranium; not so much.
Life is much farther beyond "organic materials" than a 747 is aluminum stock.
Even when you cheat and pick any point in a supposed process there is no "magic" guiding the chemistry forward. Life is not simply one "trial" that went "right", but an entire, extremely long sequence of trials with the right outcome, all of them unlikely on a cosmic scale.
All this is blithely ignored by people repeating the Drake equation. They just put in a number that makes their argument plausible without any serious consideration as to how plausible that number itself is.