If we recall our Sa'ami history (prehistory) the big breakouts were about 9000 years ago ~ just long enough after the Younger Dryas for plants to get a good start throughout the formerly glaciated areas. Have to have plants to get the game animals. So this is just short of half way back. Probably not a whole lot of people around yet, and most likely virtually everybody was free of infectious disease ~ unless they brought it with them from the more heavily populated Eastern Mediterranean.
I haven’t studied much of the Sa’ami history, I’m guessing it’s an oral tradition?