I’ve found myself in the possession of a box of old letters from the late 1920’s and early 1930’s. One of the correspondents was stationed in the US Consulate in Germany at the time. I haven’t read them myself, but given the context it occurs to me there might be some historical significance here.
Where would I even begin? Is there a process for this sort of thing?
Get in contact with museums. Especially those related to the find. For example, look for museums that focus on diplomatic history, WWII, the holocaust, etc.
It's very possible that no historian is currently interested in them, and no museum has the interest in archiving them. That's often the case with backyard finds.
But you could certainly call the museums and ask.