The director's very early, 1994 short "No Time" has made its way online. It's one of three short films he directed as part of the masters program at the AFI Conservatory (the other two were "Protozoa" -- also the name of his production company -- and "Fortune Cookie"). There's not much other detail about it online, but it's a comedy, and it's certainly very different from anything he would go on to do in his professional career. Yes, longtime collaborate Matthew Libatique is behind the camera, and it's an interesting look at the formative work of Aronofsky. Give it a spin below.
Update: Short film removed by request.