> requiring compounded infinitely improbable samples of luck to have been created
Not sure what you mean here. Evolution doesn't work by rolling all the dice at once and only selecting a winner if all the dice match some magic string. Evolution is a selective tuning process; it works (figuratively) by rolling all the dice at once and keeping the dice that do match the magic string and then re-rolling the rest[1].
[1] Of course that's not how evolution actually works. It works by selecting very tiny slightly different versions of things in a biased way. Those biased versions of things just happen to be things that can make more of themselves, and so the system automatically selects for things that good at self-replicating and surviving. Evolution doesn't jump all over the place with infinite improbabilities, it is actually a very systematic and even somewhat predictable exploration of the fitness landscape.