If we want to go to the very roots of Egypt, it would probably be a man translated as Mizraim in the King James Bible, or NIV translates his name as Egypt. Egypt was one of the sons of Ham. But it takes a few generations to build a nation.
According to Egyptian tradition, the first man of whom they had a record of, was king M'na, or Menes, who lived around 3200 B.C.
He was born in Tena (or Thinis) in Upper Egypt, where his ancestors had lived before. He was the first man to become master of the Lower Egypt, in addition to the Upper Egypt. So he was the first king to unite the two geographical parts of Egypt into a single country.
Once the two regions where unified, M'na thought the new country needed a new capital. He believed the new country could not be conveniently ruled from Thebes, or from any other location in the Upper Region. It had to be a place in the center of both regions. Nature had pointed out only one such region. It was a place where the narrow "Upper Country" terminates, and Egypt opens up into the wide smiling plain that spreads itself on every side of the sea. This location provides easy access to both regions, which makes it easier for kings to command both regions. This location also creates a safer place against foreign attacks, it could only be attacked by land.
Experience has shown that the founder's instinct in selecting the location for the capital was remarkably accurate. Although, from time to time, the power shifted to Alexandria or Thebes, the center of power kept gravitating to the location pointed out by geography.
Before building his city, the king undertook a gigantic task. He had to free the region from the Nile. The Nile flooded the wrong side of the valley. It had to be moved to the other side, so that it floods the region on the side of Asia, to create a water hedge against the Asian invaders. So he raised a huge embankment across the natural course of the river, forcing it to run in a new channel, midway down the valley or to the eastern side. Now he had protection from the invaders from the east, and a place to build his city between the river and the western hills.
It seems remarkable that such a feat was accomplished at the dawn of Egyptian civilization. But than again, the pyramids, very likely, were constructed not too long afterward. The engineering skill required to build the pyramids matches the genius found in the first king.
So the city of Menes was built, also known by a few other names, including Memphis. As a city without a temple was unthinkable to the religious Egyptians, this city had a temple in its center, temple to Phthah. Phthah was "the Revealer", the Divine artist, by whom the world and men were created. The hidden thought of the remote Supreme Being was now manifest to his creatures.
King M'na is said to have died from an attack by a hippopotamus, and as a matter of fact, the kind of hippopotamus described in Job chapter 40. But it could have been just an allegorical speech for succumbing to death by the "goddess of evil".
Historian Manetho puts the length of reign of king M'na at 62 years.
As a note, there are no carvings or monuments that have been found to prove that King Menes existed. But the embankment to divert the Nile is real, the city of Memphis is real, the temple in the city was real, and the fact that Abraham found a full civilization when passing Egypt as far back as 2700 B.C. was real.