This one should be fairly easy, at least the list of possible players is short and simple to research if you go that route.
Only once in major league history have three future Hall of Famers made their big league debuts on the very same day. Who are those three Hall of Famers who played in their very first MLB game on the same day?
Well, technically you're right, Stumpage, and I have to give you credit for coming up with those three names. All three made their playing debuts on May 5, 1871. However, George Wright and Al Spalding did not go into the Hall of Fame as players, but rather as execs/pioneers of the game. But since I didn't really specify that, you get an A+ on the day
The answer I was looking for was the following trio of players: Luis Aparicio, Don Drysdale and Frank Robinson. All three made their MLB debuts on April 17, 1956.