How might Proto-Afro-Asiatic speakers have migrated into Africa?

There is no consensus among scholars regarding the original homeland (Urheimat) of Proto-Afro-Asiatic speakers, leading to different theories on how they migrated into Africa.1

One prominent theory, supported by the linguist Igor Diakonoff, suggests that the language group originated within the Sahara. In this view, the speakers were already present in Africa and subsequently migrated to various regions, including an exit from the continent by those who would eventually speak Semitic languages.1

Conversely, research influenced by the "out of Africa" theory for Homo sapiens sapiens posits that the Urheimat was located in the Fertile Crescent of the Middle East. Under this hypothesis, Proto-Afro-Asiatic speakers migrated into Africa by crossing the Sinai Peninsula and moving through the Nile River valley. From there, they dispersed to establish the five constituent language families across the continent, including Egyptian, Amazigh, Chadic, Cushitic, and Omotic.1