Basically the title. What did greeks and romans thinkk of other ancient civilized cultures such as Egypt and Mesopotamia? Did they also think of the as barbarians and savages? Or did they have some sort of special respect for them in comparison to Gauls and other tribal cultures?
They really didn't know that much about the Assyrians, and basically nothing at all of their predecessors, and what they thought they knew was sorta mythological.
u/Trevor_Culley discusses that here:
Now that covers the inland parts of Mesopotamia but more might be able to be said about Egypt (which the answer notes that Greek mercenaries even worked for Pharaoh Psamtik I in the 7th century BC).
It's worth noting though that the Greeks did have a certain reverence for the founder of the Persian Empire, Cyrus, and their general worldview seemed to hold the Persians in a state of decline, accelerated by their defeat of Xerxes and culminating in Alexander's conquests. But they didn't REALLY know much factual history and their view of Cyrus probably wasn't entirely realistic. These are also Greeks in the 5th century (like Herodotus) writing about Persians from the prior century or so, so not really "much more ancient" like you're asking.
Further discussion on this question can be found over here.