I'll have to say my first play ever was OUR TOWN or PYGMALION (whichever came first) at my high school. It's actually hard to imagine seeing either of those, or anything else, and thinking, "This is my first play!" But I'm not dredging up anything that's likely to have been earlier.
First professional play was probably LUV on tour at the Coconut Grove Playhouse in Miami. At least that seems to be the earliest program I have. It's dated August 1965 and starred Tom Bosley, Dorothy Loudon, Herbert Edelman, and was staged by Jack Sydow. I was a late starter, as we lived in Fort Lauderdale and it was a haul getting to any theater prior to the construction of the Parker Playhouse right there in town.
First play on Broadway was SLEUTH, early summer of 1971, starring Anthony Quayle, Keith Baxter, Philip Farrar, Harold K. Newman, and Roger Purnell.
Clifford Williams directed.
Side note: It's likely that the Columbia recording of LUV was my first play on record. What I don't recall is which came first, seeing it or listening to it. I just know I took to it from the start. The other early recording I thrilled to was VIRGINIA WOOLF, but that was done surreptitiously at the library. I didn't think I dared buy that one and play it in the house!