I highly, highly recommend Tides of History podcast by Patrick Wyman. He has a long arc on the late Bronze Age, as well as a bunch of other looks into early historical states like Egypt. One interesting tidbit from the Bronze Age arc is the large number of advanced contemporary states in the Mediterranean / Near East world, of which Egypt was but one (but perhaps one of the most powerful and oldest).

Of course, there’s also China, who by end of the Mediterranean Bronze Age, was a series of massive, advanced states as well, and India, which I know less about.

I wouldn’t go so far as to call Egypt the greatest ancient civilization, but during its very long peak, it appears to have been pretty incredible. But again, comparing with other kingdoms and entities can be difficult as there’s a bit less understood on them.