Evolution isn't looking for that sequence.
It is looking for any change in sequence with a positive payoff, and in the meantime constantly diversifying sequences with similar outcomes, creating more opportunities for serendipity.
Every large animal is born with mutations. So we are also quite robust to spreading the search, running multiple experiments at a time, taking small risks with genes not quite as good, which will get weeded out quickly when combined with other weaker genes, but in the meantime cast a wider net for meshing with another gene that complements it.
So yes, in any given species with a nontrivial population, millions or billions of genetic variations are being explored at any point in time. We are nothing like carbon copies of each other, differing by just a couple checkmarks.
This is a radical speed up. Just as sexual recombinatory reproduction is. Evolution today operates with vastly more efficient genetic environment, structures and systems than what early life did.
Tractable statistics do no justice to how biology works and all the paths it searches. I am not knocking formal statistics at all, just noting that past one or two step events, the layered statistics of chemistry, genes, gene clusters, epigenetics, populatoin dynamics of complex creatures in their complex environments, etc. are not going to be tractably modelled.
Measurable sometimes for sure, but not symbolically characterizable or calculatable.