Welcome to FT. If you really are totally flexible on dates and origin airport then you may have some options. But keep in mind that this is the first full year that Japan is open for general tourism so deals will be harder to find than in 2019.

Check the premium fare deals forum on FT, there are occasional deals to Japan or to nearby cities (ICN, TPE, etc.) from which you can backtrack to wherever in Japan you are heading.

As others have suggested, Google Flights will be your friend. You will tend to find deals to Japan from LAX, JFK, YYZ, and YVR, all of which are big cities with a lot of competition. This requires a positioning flight as well as transit through Canada in the case of the latter two. Google Flights lets you search from up to ~6 origin cities at once which makes things more efficient.

Finnair has offered decent deals to Tokyo and other cities in Asia from JFK for ~$3k, with a long layover in HEL.