The best explanation is a superior cross breed of humans. Think of two tribes, each of which have several useful adaptations or mutations, but when one of each of their number mate with the other ones, they produce children far better than either.
Smarter, stronger, healthier, better metabolism, the kids just run circles around their parents, and the tribe soon dominates, and spreads its genes to other tribes in the region.
A good possibility is an imperfect mutation for high intelligence. There is some speculation that a lot of what we consider intellectualism is a fairly recent development. However it is imperfect because too much of the mutation can have the opposite effect of retardation.
But at that time, an average IQ of 20 to 30 points higher in a tribe would easily result in it becoming dominant.
But almost as important is enhanced fertility, so that there are an increasing number of smart kids running around.
It's just a matter of time and they'll pin down the genes necessary for people to read and write, then they'll trace the paths taken by the ancient scribes!
BTW, those guys always had jobs. Although dyslexia was probably the standard condition, the leadership elite could see the value of writing instantly. The scribe class/caste would be protected.