Not even Greece existed prior to the early 1800s let alone a Greek church!
And there are no known Greek disciples of Christianity because they were well known idolaters and continued to be so for a very long time well into the first millennium AD.
Of course, location had a lot to do with it because Greece was too far away from the religious “action” whereas Cyprus is right next to the Holy land.
By the time a "Greece" was manufactured in the early 1800s there were some 2 million Ottoman turncoats and 2 million odd mixed Albanians, Slavs, gypsies, and others to form the modern “Greece” that you know of today!