The greeks had colonies everywhere. Odessa and Marseille started as greek colonies. They copied the phoenician model of "where there is sea, we can colonize, reinforce, conquer and trade with".

https://en.wikipedia.org/wiki/Greek_colonisation

And then Alexander the OK conquered the "entire" world. After his death, his empire was split into multiple hellenic(ie greek) kingdoms. Greek became the lingua franca, since the ruling class was greek, and greek culture was spread everywhere. Thats why the New Testament was written in greek.

Hanukkah is actually the celebration of the uprising of the jews against their greek rulers. If you are somewhat familiar with the history of the era, you might have heard about the Seleucids or the Ptolemies. Those were greek kingdoms. Cleopatra was a Ptolemy and she was the first in her dynasty who bothered to learn egyptian. All previous Ptolemy rulers only spoke greek, their court was greeks and some hellenized(greekified) jews and egyptians. The Ptolemies were extremely incestuous.

Then the romans came and conquered most of that. Some other greek kingdoms were taken back by their local population. Funnily enough, the last independent "greek" kingdom that survived was the most remote one, the Indo-Greek Kingdom.

https://en.wikipedia.org/wiki/Indo-Greek_Kingdom

An indogreek kingdom that fought chinese raiders. Thats an interesting crossover.