53-50 thousand years ago.
The broad outlines of the spread of Homo sapiens have been established for several decades now: origins in Africa, expansion out of Africa at least 50-45 thousand years ago. But we’re still arguing about the details. Just this year it’s been reported that modern humans reached Sumatra 73-63 thousand years ago, and that stone tools in Australia date back 60 thousand years ago.
Also, based on recent recalibrations of DNA mutation rates, it looks like the African/non-African split might have happened more like 100 thousand years ago than 50 thousand years ago. So the ancestors of non-African (or non-sub-Saharan-African) H. sapiens might have occupied a homeland somewhere north of the Sahara between 100 and 50 thousand years ago, before spreading through Eurasia. North Africa is one possibility. The Near East, maybe the Arabian peninsula, is another possibility. The (or “a”) homeland might be (gated, sorry) underwater, under the Persian Gulf (sea levels were lower then). Both possibilities have some archeological support. There might have been multiple homelands, and multiple expansions – south through Arabia and along the shores of the Indian Ocean, and north through the Levant and into Europe.
A recent (2015) redating of archeological finds suggests that the Levant-to-Europe corridor was part of the story. A modern stone tool technology, coming from Ksar Akil, just outside Beirut, Lebanon, dates to about 50,000 years ago, a little before much the same technology appears in Europe, in the form of the Upper Paleolithic.
And many other “details” remain to be resolved: What did interbreeding with non-sapiens mean for the evolution of H. sapiens? And just what advantage(s) did H. sapiens have that allowed him (us!) to replace other species? Stay tuned for more on Logarithmic History