Incredible to think how something this intricate with so many interdependent parts and integrated systems could have evolved.
In a given teaspoon of ocean water in the top layer, there are millions of bacteria (in soil there can be up to 1 billion). Each one lives for a day or two before it either divides or is consumed, with a handful of mutations at each round of division. So ~200 divisions a year, for three billion years, with selection stochastically whittling out the few good mutations the crop up now and then, in a diversity of changing ecosystems and you end up with where we are today. Oh, and the occasional horizontal gene transfer for extra spice.
Obviously that is a large hand wave -- the numbers above are from today's environment; early on the biotic density was lower. But the large numbers swamp things. The only real mystery is how things initially got started. But again, it is hard to imagine the time scale involved and the wide variety of environments that exist over the time to imagine the happy accident where the first self-replicating molecule just happen in the right environment that was stable enough for long enough for that self replication to gain traction.