Yes, the more I search, the more I see two lines of scientific thought on the emergence of behavioral modernity: National Geographic and Behavioral modernity - Wikipedia show the idea of a it appearing suddenly 50,000 years ago, followed by an immediate “out of Africa” migration. (This provides a solution to my concern about it happening before the out of Africa migration.) Both articles point out the other theory which has a much earlier appearance in Africa. As you said, it could be that there was a ‘running start’ to the leap. Certainly, there was not a consistent, continuous appearance of modernity until at least 50,000 years ago.
At any rate, it would be a big mistake at this time to get wedded to a too specific time period or to any other non-essential aspects of the theory.
DougK