I am not sure if it was the first .... but in the Spring of 1996 a sophomore girl named Kelly Snelson played second base on her boys varsity hs Baseball team (Rosebud HS, Rosebud Ark). She earned national attention and a write up in Sports Illustrated by "belting a 300 foot grand slam home run over the right field fence in Rosebuds's 13-4 victory." She was apparently a great athlete having been the MVP of her softball and volleyball teams the year before - so the baseball team recruited her to play and the move paid off! :-) Also around the the same time period the Colorado Silver Bullets were a team of profession female baseball players who played against men's teams - Kim Braatz, Pam Schaffrath, Lisa Martinez and Tammy Holmes all hit long home runs over the fence on full sized regulation fields. Girls have been playing baseball for 100 years so these were most likely not the first homers ever hit by girls .... but they are the first to be well publicized.
Dolph Camilli hit the first ever televised home run as the Dodgers beat the Reds 6-1.
On April 10, 1971, Don Money of the Philadelphia Phillies hit the first home run in Veterans Stadium.
He hit his first career home run against the Los Angeles Dodgers on April 22, 2004.
The first home run hit at Jacobs Field was April 4, 1994 by Eric Anthony of the Settle Mariners.
Doug Ault hit the first home run in Blue Jay history.
Daniel Sepic of Pennsylvania hit the first ever home run.
Babe Ruth hit his first home run in 1915. As he was born in 1895, he would be 20 years old when he hit his first home run.
Travis Lee (who???) hit the first home run in the first regular season home game played on March 31, 1998
Mulder was the first pitcher to hit a home run at the new Busch stadium!
Babe Ruth hit his first home run in 1915 with the Boston Red Sox.
The first home run at PNC Park was hit by Sean Casey of the Cincinnati Reds. The first Pirates Homerun was hit by John Vander Wal.
I
Dolph Camilli hit the first ever televised home run as the Dodgers beat the Reds 6-1.
No, he hit a walk off home run in his first major league game but it was not his first at-bat.
On April 10, 1971, Don Money of the Philadelphia Phillies hit the first home run in Veterans Stadium.
He hit his first career home run against the Los Angeles Dodgers on April 22, 2004.
The first home run hit at Jacobs Field was April 4, 1994 by Eric Anthony of the Settle Mariners.