I've heard that Gertrude Stein (herself a lesbian) is usually credited due to some of her writing in the 1930s or 20s. That sounds too good to be true, but the 1890s were widely referred to as the "Gay Nineties," so it seems unlikely that was common usage long beforehand.
Whilst it doesn't trace early uses of the word, answers by u/cdesmoulins and u/sunagainstgold in this recent thread discuss some of the terms people used to describe themselves at that time.
The term the "Gay Nineties" wasn't used specifcally to refer to sexuality. See this answer by u/chocolatepot for some discussion of 1920s nostalgia for the 1890s.
I have an earlier answer about the double meaning of "gay" that might be relevant to your interests! It's worth noting that the colloquial meaning of the word wasn't necessarily in wide circulation outside gay subcultures until much later; the innocuous sense of a word like "gay" had to be relatively commonplace for the word to have maximum utility as a litmus test for whether somebody else was in the know regarding gay life. The colloquial sense of the word wouldn't approach the popularity of the straight sense until quite late in the game, even until the 1970s, and that's when you start to see people shying away from using the word "gay" for fear of an accidental double entendre. People still described strange things as queer, or cheerful things as gay, well past the point where those words had an established colloquial meaning among people in the know.