Was yogurt made by the Greeks?

Only Greek yogurt.

It is believed to have come from Mesopotamia. Although it may have come from Mongolia. There is speculation that Mongolians who carried yak milk in skins while on horseback may have discovered the first kefir type yogurt drink.

No, it’s made by Bulgarians.
Joke aside, it came to Balkan from Turkey, if I remember well.

I think yogurt was around in the days of the Pharoahs. It almost certainly paralleled the discovery of cheese, because milk is so distinctly perishable.