In a 1984 interview, Julius Lester asked Baldwin about his early days after the war as a writer publishing reviews and essays "for publications like The New Leader, The Nation, Commentary and Partisan Review" Baldwin described the people he met through these publications as a kind of "Olympus":
"Dwight MacDonald told me that I was "terribly smart." I certainly learned a lot from them, though I could not tell you exactly what I learned. A certain confidence in myself, perhaps."Out of curiosity, I looked up all the bylines where Baldwin originally published the essays in his now classic first two collections, Notes of a Native Son and Nobody Knows my Name. Here they are: Commentary, Harper's, New Leader, Partisan Review, The Reporter, The New York Times Book Review, Encounter, The New York Times Magazine, Esquire, Le Preuve. The Fire Next Time was published in its entirety in the New Yorker, Baldwin's first published essay in a national magazine was for The Nation, where his later work frequently appeared, and he was on their board during the last years of his life.
Of course no recent particular event and no particular magazine of note that maybe would have been predisposed to miss the work of an African-American who is probably the greatest essayist in American history and any prominent "serious" publications missing from the list are just a coincidence.
(The limitations of my library's archive are such that I haven't been able to confirm if Baldwin ever wrote for the publication that shall not be named. If so, would be very curious to see where and when.)