Well I figure they have carbon steel weapons... everyone around them has carbon steel weapons... who doesn't have them? The folk northward. The historical food producing cultures in that area would fall like grain under a scythe

where in OTL they provided a buffer to stop expansion. I am turning a 500 year process into a sorta 10 years everyone just leaves this place thing though, I do admit. I guess we could slow play it and have them turn up in time to crash the Jesus party.
It's pretty much just for fun though, rather than super serious. Regards the logistics, pastoralists would do alright along the Nile - the Turks had the disadvantage of being pulled in other directions and being in the period of post-berber saharapocalypse thanks to the goat spam. The Greeks and Romans both had no carbon steel and the Arabs had to face off against organised Christian Ethiopia/Axum and so on - they kinda got bogged down in the highlands rather than going along the Behr el Ghazal and into Central Africa.