Can I travel directly to Schengen from my domicile country with my Greek green card?

Greek permanent residence cards can travel freely in 26 Schengen countries. However, there is a time limit, 9 days in half a year and 18 days in a year. Limited to stay, unable to work, live and settle down.

So you can travel. If your domicile country is China, you can travel directly from China to Schengen countries.