There have been two migration events out of Africa. The first was the expansion of H. erectus into Eurasia approximately 1.9 to 1.7 million years ago, and the second, by H. sapiens began during the MSA by 80 – 50 ka MSA out of Africa to Asia, Australia and Europe. Perhaps only in small numbers initially, but by 30 ka they had replaced Neanderthals and H. erectus.
Two migrations out of Africa have been documented: the first involving the expansion of H. erectus into Eurasia about 1.9 to 1.7 million years ago, and the second, by Homo sapiens beginning during the MSA (Middle Stone Age) between 80-50 ka from Africa to Asia, Australia, and Europe.  Initially small in numbers, they replaced Neanderthals and H. erectus by 30 ka.