Transmission between the two societies at the earliest stages has not yet been decided. Did Mesopotamia (Uruk) feed Egyptian civilisation, stimulating writing? Uruk traders reached into Anatolia in the 4th millennium, but did they reach Egypt too?
The first Egyptians: is this known or needs investigation?
An apparent change in climate about 5,000 years ago created the Sahara desert and diverted the (later Nile) river to go through Egypt. Then people moved in around the river. Homer calls the river Aegyptus (Egypt), that was its name at the time.
I think the southern Mesopotamian civilization came before the Egyptian one.
A study could be on the transfer of new ideas from Sumer to Canaan and from Canaan to the West with the Phoenicians navigators from 3.000 BC.
The arch in architecture, the wheel, the lyre, the trading system with bartering, the calendar of the year(12 months), the month of 30 days, the hour of 60 minutes etc…
Another subject could be The Phoenicians and the formation of the Western World. Cultural diffusion, navigation, shipbuilding, glass, purple dye, alphabet…