Albert,
I believe the cultural great leap forward had everything to do with the discovering of farming and the tendency of people groups to congregate into cities. Farming wasn’t discovered everywhere simultaneously (I may be wrong but I don’t believe Australian Aborigines farmed and I know for sure that the African San people remained hunter gatherers). After it was discovered in fertile valleys (like Mesopotamia, along the Nile and along the Indus valley), it spread very quickly to the rest of the Middle East and then to Europe.