Can I fly to Japan with an American green card?

No, Japan only looks at everyone's entry passport. Even an American green card is distinguished by the nationality of the passport, which means that holding an American green card is not a condition for Americans to enter the country. There is only one exception: Japan has a permanent resident who is similar to an immigrant. This kind of person is not Japanese but has the entry conditions of Japanese citizens. Moreover, even American citizens cannot guarantee that they will definitely enter Japan. Japanese law only fully protects the right of Japanese citizens to enter Japan. Even American citizens who have committed crimes in Japan before or have other bad records (smuggling and the like) can be refused entry to Japan.