There were two big waves of colonization into europe in the last 8000 years. The first wave was anatolian farmers—who started coming westward 5000-6000 bc. (the second group nomadic herders from present day ukraine who started coming westward about 3000 BC.)
its unlikely that the first group of anatolian farmers only went westward. more likely they also moved southward into syria israel and egypt—as well as southeast into mesopotamia.
The Anatolian Farmer Hypothesis was discarded, even by its own creator, in favor of the Yamnaya hypothesis.
Then there were the Anatolian farmers who build Gobeki Tepi and another, even earlier, site between 13,500 and 10,800BC. But none of them were Greeks, which was the subject of my post.