Life is not 'self replicating proteins', but rather self-replicating processes. And in those processes, hundreds of chemical components are involved in a dynamical manner, which requires both spacial (chemical formula) and time synchronization.

And as life complexity increases, so does the the complexity of the processes that make it possible. Humans are the result of a huge number of individual, albeit not all independent, events, each with a very low probability. Multiplying those probabilities, as it's required when determining the probability of occurrence of a sequence of independent events, yields numbers that are hard to event write down without special notations.

As I see it, the only way out is to postulate evolution based on other non-probabilistic evidence, and then to conclude that in spite of the low probability those events still happened.