Absolutely George M. Cohan, who was a star 30 or 40 years before Gene Kelly appeared on the scene. But I doubt Cohan was the first: there were triple-threat minstrel performers as far back as the early 1800s. We just don't remember their names because there were no movie cameras to film their work.
I suspect GavestonPS is right. Plus, it reminds me of a comment an actor made (in one of the "That's Entertainment" movies maybe?) where he said in the studio days MGM expected an actor could sing, dance and act. I would that that would be even more true for stage performers who needed to be ultra versatile to get work.
This came up because my daughter and I were talking about "Small House of Uncle Thomas" which has a dancing ensemble, a singing ensemble and one actor. I explained to her that this used to be the way most Broadway shows were written until the 1970s (with some exceptions). So, I was specifically wondering about people in Broadway shows- not film nor minstrel shows - (Rooney didn't make it to Broadway until 1979). And since I (nor likely any poster other than After Eight) have any idaa what kind of an actor Cohan was, Gwen Verdon was the first name which came to my mind of someone who did it all back in the Golden Age.