This depends upon how we define civilization. Think of what comes to mind when you mention the word "civilization" in the context of human history. You probably think of cities, domesticated animals and agriculture, reading and writing, politics, mythologies, that sort of thing. Do all of these things have to be present, at the same time, in order for it to be called "civilization"?
I think the most important aspect of the anthropological definition of civilization is "domination over the environment". This means agriculture, animal domestication, shelter, all leading to a sustainable or growing human population.
Very, very ancient Egypt has probably been continuously inhabited by humans and human ancestors for an indefinite amount of time. The Rift Valley region where humans evolved was a convenient pipeline into Egypt, although the cultures that dwelled there were probably hunter-gatherer "uncivilized" types that left few relics.
Egypt has always been significantly affected by the Nile, but Ancient Egypt was also strongly influenced by the Sahara. 8000 years ago, the Sahara was nowhere near as dry as it is now, and ancient Egyptians were able to settle in areas far from the Nile. As the Sahara grew, and the climate dried out, Egyptians were forced closer and closer to the Nile, relying even more heavily on it for everything. This means that ancient Egypt probably developed its civilization over a large area, which then condensed along the Nile.
"Civilization", in the sense of pyramids and pharaohs, began around 5000 years ago, but by this time all of the hallmarks of civilization such as writing, domesticated animals, agriculture, and religion, were already in place. Because of this, it's not really possible to say it "began" in a particular place, but we could say that the city of Nekhen was the largest and first capital city and the most likely center for civilization in the region.