The Great Leap occurred 65,000 years ago, but not all groups participated equally. According to the author, the "humanity" was there in all of them, and they were all capable of making the leap (this I doubt), even if their group didn't do much with that inherent ability. They all may have begun using spears, etc., around the same time, but it's fairly evident some merely copied their neighbors, not invented new tools.
Credit for IQs above 80 is owed to the fierce competition with the Neanderthals. Killing them off was essentially an IQ test of increasing difficulty. No peace treaty was ever possible with them so it was kill or be killed. Africans did not participate in this 20,000 year war, which is reflected in modern genetics.