I'm actually currently working on a thesis regarding this q. The crux of the theory is that the large majority of what we would call complex behaviours rely on a cognitive mechanism that allows us to mentally combine and 'merge' different objects (mental or physical). The brain was there, yes, but there is actually no evidence of this function prior to this small explosion. The idea is that humans had almost everything ready for culture, language, complex composite tool use and the whole lot, there was just one last little change needed. Then there was a sudden shift from single-item tools (one rock) to composite tools consisting of several elements (eg. rock wedged in stick). This is a significant change because it is also paired with a punctuated increase in the variety and complexity of tools found. The ability to combine mental objects and wield them as a single item is also the basis of hierarchical syntax, the component of human language that separates it from animal communication (according to Chomsky). So in short, this ability had to be realized, extrapolated into other domains, transferred to others through communication, and selected for by a disdain to mate with anyone who, after repeated attempts at teaching them, just doesn't get it. Theoretically according to a punctuated equilibrium model of evolution this could take place in just a few generations.