Indeed. Regular interaction in the region at minimum went from well from modern day Lebanon and down through Ethiopia (Kush). In the biblical timeline Moses had a Kushite wife. I have read a compelling account that links biblical Moses with a possible identification as Senenmut during the New Kingdom Period and connected with Hatshepsut (possibly Pharoh's Daughter). Following this period we know there was regular political and military correspondence from all over the region, such as the Amarna letters which are on display at the British Museum. The point I make, as a lay person who has read the biblical narratives and other sources, is Egypt was extremely well connected for an extremely long period of time and significant DNA mixing the entire time is to be expected and I doubt tells us too much about origin migrations.