Turning the question around, here are some homers by players not yet born when the pitcher debuted in MLB. This covers years 1973-2004.
07/13/1986 - Ruben Sierra off Phil Niekro
09/13/1986 - Jose Canseco off Phil Niekro
05/31/1987 - Mark McGwire off Tommy John
05/31/1987 - Mark McGwire off Tommy John*
07/05/1988 - Ruben Sierra off Tommy John
09/19/1990 - Ken Griffey, Jr. off Nolan Ryan
06/22/1990 - Ken Griffey, Jr. off Nolan Ryan
04/26/1991 - Carlos Baserga off Nolan Ryan
07/28/1991 - Travis Fryman off Nolan Ryan
05/26/1992 - Ivan Rodriguez off Charlie Hough
08/27/1992 - Kevin Koslofski off Nolan Ryan**
06/22/2002 - Vernon Wells off Mike Morgan
* - Not a mistake; Big Mac got him twice on the same day.
** - 5 times might just be a record for these chronological indignities.
Looks like there’s just five more in the Retrosheet Event Files which go back [incompletely] to 1957.
08/21/1962 - Boog Powell off Early Wynn
09/28/1962 - Joe Pepitone off Early Wynn
06/21/1964 - Rusty Staub off Warren Spahn
04/30/1965 - Tony Perez off Warren Spahn
08/31/1965 - Alex Johnson off Warren Spahn