That's buried quite deep in the rules that underlie chemistry actually. And there are many other rules and behaviours behind biochemistry too, whether it be the properties of water as a solvent for life, the unique ability of carbon atoms to "catenate", i.e. form long chains, or a myriad other things. Nobody on this thread is suggesting the uncertainty principle is any sort of key to the origin of life. The point being made is the more general one that, in nature, order arises perfectly naturally from random individual interactions, owing to the laws of nature that govern everything.
So one needs to abandon the notion with which you started this thread, of there being simple alternatives, between either "predetermination" on the one hand, or "accident", on the other.
If you now want to ask questions about how life arose on our planet, join the club. So do we all. Nobody knows, yet, though we have a lot of tantalising clues. What we can say is that all our experience of nature is that simple random things can and do result in more complex ordered structures. This gives us faith that there is a natural answer out there to be discovered, one day, once we have enough pieces of the jigsaw. That is how science will approach the issue.