Wow, there are a lot of threads to pick apart here.
First of all, as Ilona has said, Classical Antiquity is not really one unified thing. It's more of an idea reconstructed by scholars in the nineteenth century. One can find a lot of distinctions between, for example, Greek and Roman sculpture, but early art historians didn't know that. They were trying to create a linear history from scattered archaeological specimens, and they lumped them together as "Greco-Roman." It's true that Roman culture was influenced by the Greeks (and the Etruscans, the Egyptians, the Persians, etc.), but the two are still distinct from each other.
Now, on to foreign influences on the Classical Greeks (roughly defined as Greeks of the 6th-4th centuries BCE). It's not precisely true that the Greeks "stole" everything from Asian and African societies, but there were influences there. Societies all around the Mediterranean were in frequent contact with each other during the Bronze Age (ca. 3000-1200 BCE), but at the end of the Bronze Age, the regional trade network collapsed, and there was less cross-cultural contact. People moved away from cities and produced less art and fewer written records. The original Greek written language died out entirely. It's not a coincidence that all of this happened around the same time, but scholars are not sure of the exact sequence of events or what caused the end of the Bronze Age.
The centuries after the end of the Bronze Age are known as the Greek Dark Age. People were still living in Greece, but we know relatively little about them, because they produced fewer artifacts than the people living in periods before or after--at least, they produced less that has survived to the present day. When they started producing art and writing again, around 700 BCE, it was clearly influenced by Near Eastern cultures--so much so that historians in the 19th century named this time the "Orientalizing Period." More politically-correct scholars call this the Archaic Period.
Look at this sculpture from Ancient Egypt: https://en.wikipedia.org/wiki/Ranefer_(High_Priest_of_Ptah)#/media/File:Statue_Ranefer_Petrie.jpg
Now, look at this one from Greece in the 6th century BCE: https://en.wikipedia.org/wiki/Kouros#/media/File:Kouros_anavissos.jpg
Now, this one from the 5th century BCE: https://en.wikipedia.org/wiki/Contrapposto#/media/File:Doryphoros_MAN_Napoli_Inv6011-2.jpg
See the progression? The Classical Greeks put their own spin on the ideas that they got from other cultures, but that exchange of ideas happened.
And, by the way, the Greeks were not unique in terms of the cultural changes in the Classical Period. The period from the 8th through 3rd centuries BCE is sometimes called the Axial Age--all over the world, new systems of belief developed very suddenly during this time. (https://www.britannica.com/list/the-axial-age-5-fast-facts)
Classical Greek civilization, like all civilization, developed over a long time from lots of different influences. Some were European, some weren't, and the Greeks reinterpreted foreign ideas to fit with their own view of the world.