No, as a matter of fact, they weren't. According to their
Golden Age origin, the Amazons were a race of powerful women who lived in a land called Amazonia until they were conquered and forced into slavery by Hercules. According to the 1986
Who's Who,
Amazonia was located on the coast of the Black Sea in what's currently Turkey, which is consistent with the Scythians and other cultures that the Amazons of myth were based on.
For that matter, the post-Crisis Amazons
aren't Greek either. Their culture was founded by the Olympian Gods, yes, but they were resurrected from the souls of women all over the world who had died unjustly at male hands. And in the current New 52 continuity, the Amazons are the daughters of Hera, who gave birth to them on the original Themyscira (the modern name for Amazonia), the one in Turkey for which the island was later named.
So the Amazons may have a lot of culturally Greek elements, and they worship the same (actually existing) gods as the Greeks, and I guess they speak Greek (but so did the Jews and early Christians of Roman times), but the fact is, they have never been portrayed in the comics as ethnically or politically Greek. They're more Greek-adjacent, a neighbor culture to whom the Greeks were adversaries and assimilators. Which is what I've been saying all along. The fact is, the comics Amazons are closer to the mythic Amazons than I've thought.