Well, this happened to my team in my fictional league, now in its 51st season...
This guy just got called up from the minors after nine seasons on the farm, never really did much except for that season and a half in Double A about five years back, and proceeds to pitch a no-hitter in his big league debut against the best team in the league, in a duel with 1999 Angel Regalado Award winner (best pitcher) Eric Magyar, who only allowed two hits. So this was no cheapie.
Gotta feel for my DH, Andy Perez. Hey, Andy, what happened in your big-league debut? "Oh, we got no-hit, no biggie..."