The nomenclature of cultures and civilizations

Yes, cities, since civis is latin for “resident of a city”, hence civil and civilization. Starting with Ubaid & Uruk in Sumer 6200BCE and Susa in Elam 4200BCE, but Mesopotamian culture doesn’t have cultural continuity (the Assyrians might count, but they are not as ancient). You could also use the first written records as the marker.

Susa I (4200BCE) is older than the Egyptian First Dynasty, or even Lower Egypt (3600 BCE).

The Indus Valley cities of Mohenjo-Daro and Harappa are older still (6000BCE) but whatever Narendra Modi believes, there is no cultural continuity with India. That said both India and Iran were subject to Aryan migrations, so I’d agree the cultural continuity of Iran is also debatable, whereas that of Coptic Egypt isn’t.