If you go to Japan to study for a master's degree. If I study in Japan, can I apply for a green card after the graduate stage?

Green card? There is no such thing in Japan. Japan is not an immigrant country.

Sign a two-year master's study visa

If permanent residence is a permanent visa, if you want to live in Japan for more than five years, the study visa is not counted, which means that five years are counted from the time you take office. In fact, it usually takes about 10 years to get approval, otherwise it may be rejected.

Naturalization is easier than permanent residence.

The quickest way is probably to marry a Japanese.