Did Ancient Civilizations Have Their Own Ancient Civilizations?

In history class we all learn about "ancient civilizations", like Greece, Persia, Babylon, and Rome. Recorded history, however, starts several thousand years prior to Greece or Rome, for example, being around. So, what did they know about the past? Did ancient civilizations have any ancient civilizations of their own? Sources: A History of the Ancient Near East, Marc Van De Mieroop A History of Babylon, 2200 BC - AD 75, Paul-Alain Beaulieu Reign of Nabonidus, King of Babylon, Paul-Alain Beaulieu Babylonian Archaeologists of the(ir) Mesopotamian Past, I. J. Winter