Man of Honour
The thing that gets me is that this could have happened at any time over the last 150,000 years or so. People have been much the same. Same intelligence, same thoughts, same loves and hates, same inginuity, and so on, for all that time. What made it just happen then?
Genius and luck, probably. Many advances have come from a person observing what many others have observed and, unlike them, deducing something from that observation and experimenting to test that hypothesis. My favourite example is Eratosthenes calculating the size of the earth from a stick. Someone told him that in a particular town (I forget the name of it) at midday on a particular day of the year you could see all the way down a well with no shadows cast by the walls of the well. Many people had observed that over the years (everyone who had ever lived in the town, just for starters) but it was Eratosthenes who used that observation to deduce that the difference in lengths of shadows from sticks of the same length in different places at the same time could be used to calculate the size of the Earth. The only inaccuracy in his method is that it relies on the assumption that the Earth is a perfect sphere and it isn't quite. Getting back from my meandering...my guess is that over the millenia quite a few people would have observed seeds falling and plants growing where the seeds fell but only a few hypothesised that it would be possible to make plants grow where you wanted them to by planting seeds. An obvious idea in retrospect, but not until someone had thought of it and successfully confirmed it by experiment. Why would a hunter-gatherer think of planting crops anyway? It was a radically new and different idea to them, as strange as, for example, the germ theory of disease was somewhat more recently. Or even more recently, a programmable general purpose computer. It's such a routine thing now that toddlers understand the general concept, but when Babbage invented it he had enormous difficulty explaining what was then an utterly bizarre concept to anybody and only had any significant success by over-simplifying it as an automatic calculator. His response to the Countess of Lovelace's letter is joyfully enthusiastic because he was so delighted to find someone who really understood the idea.
(But then, in the same way, many human groups must have crossed the red sea at the "Gates of Grief" over time. But the genetic record strongly suggests that just One (AND ONLY ONE) of those groups went on to become the ancestors of ALL non-African Humans!!)
It is quite staggering really!
I'm not so sure that many human groups left Africa, by any route, in the ancient past. It's not like Africa was short of space for the relatively few humans alive back then. Also, I think it's not certain that all humans outside of Africa are descended from the same group who left Africa together. I don't think we can nail the timing down anywhere near that precisely, nor the lineage. For example, if a woman had no daughters then using mDNA to trace maternal lineage won't get to her.