Countries With the Largest Air Forces

Do you mean the last century or so? Greece wasn't even a country more than 200 years ago. At the time both the territory that is currently Greece and the territory that is currently Turkey were part of the Ottoman Empire. They've pretty much hated each other ever since bother countries came into existence, but not before. Unless you're trying to conflate Greece with Sparta and Turkey with Troy or something truly bizarre like that. :D But those were not the same people. Nationalist creation myths are always a lie.

This is a false but commonly believed lie. Nationalism is a lie. There are not distinct, discrete, cogent groups of people connected by common heritage, language, religion, genetics, etc that have existed in the same arrangements for thousands of years. This is part of the nationalist fantasy. While there were "Turkic" people in Central Asia that invaded Anatolia, speaking languages related to modern Turkish, those are not the same people who live in Turkey today. And while there were "Greeks" in the Ottoman and Byzantine Empire, the label did not mean the same thing at those times. Turks and Greeks did indeed appear out of nowhere, at around the same time, right around the middle of the 18th century- the same time that Macedonians, Bulgarians, Germans, Italians, Russians, Chinese, etc. as we conceive of them today also appeared.

"Greek speaking" people of the Byzantine Empire were not Greeks, the way you're using the word, any more than Jamaicans are English, or Mexicans are Spaniards. I know that this goes against the nationalist myth of Greece, and because nationalism as an idea is so deeply ingrained and commonly accepted today, I also know that this seems counter-intuitive.

No. A nation itself is an absurd notion. The idea that "Greeks" today are the same people as the "Greek"-speaking people of the Byzantine Empire, or the "Greeks" of ancient Athens, that's absurd. The whole concept of nationalism is a lie built on a fallacious and tribalistic concept of how history works. AND, this concept did not exist prior to the 18th century when the concept of nationalism was invented. THIS is when some subjects of the Ottoman Empire decided, hey, all of these many different disparate people around the empire who speak a language basically the same as Greek, and go to Greek Orthodox Christian churches, they are all the same people, and they have all descended from Alexander the Great and the people of ancient Greece, and they all share the same history and culture and genetics, and they should come together and form their own country where they will be self-ruled on land that belongs to them by genetic birthright because of some ancient lineage.

This was a completely new concept in the 18th century, and it's completely BS. The same concept inspired Bismarck to unite all the "German" people, and Garibaldi to unite "Italy", and spelled doom for the multi-ethnic Ottomans. But it is based on fantasy, not reality. So... yes... these nations did not spring in to being until they were imagined to have existed. They did not exist prior to that inherently. Nationalism is a social construct. We are all the same people. We are all the same race. Tribalism is evil in addition to being simply wrong.