Evolution & Combinatorics

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Recently, I was challenged by this question (by a creationist, mind you):

"Humans have about 3.2 billion DNA base pairs (bbps). The number of
possible combinations is roughly 2^(3*10E9), which is "essentially infinite".
Following only ~4.5 billion years of life on this planet, how could
evolution already have arrived at the current configuration given the
huge size of the combinatorial space created by our 3.2bbp's (DNA)?"


I have always thought of evolution as a kind of "random search", a kind of "algorithm" that explores many of the possible DNA-combinations.
But considering the vast number of base pairs in our DNA, that seems unlikely to work out (even if we assume a short average lifespan and very large populations).

I have had some thoughts on this:
1. The average proportion of favorable to unfavorable mutations could be high, and the distribution highly uniform.
2. "Inefficient" encoding (evolution may not favor "compression"), redundancy and epigenetics. The "core human DNA" (our 'blueprint') may be much smaller than 3.2bbps.
3. Evolution somehow accelerated or is accelerating. Perhaps genes ("DNA modules") are readily reused and recombined, promoting new endophenotypes and phenotypes, even complex ones, with few mutations (think of cells; we have ~200 types).
4 ...


I'm interested in understanding and learning more about this (especially book recommendations).

Any pointers would be greatly appreciated.