No, he hit a walk off home run in his first major league game but it was not his first at-bat.
Babe Ruth
pujols
In MLB, that was Babe Ruth who hit his 600th home run in the 1931 season.
The first home run in MLB history was by Ezra Sutton of the Cleveland Forest Citys on May 8, 1871 against the Chicago White Stockings in the National Association. Sutton hit a second home run in the game to be the player to hit the first and second home runs in MLB history.
Not in MLB ... although he did hit his first MLB home run in his 3rd ever at bat ... it was a grand slam.
Alex Rodrigez
Mark texiera, with 39 home runs
Babe Ruth
Mantle
The record is still held by Barry Bonds.
In MLB, that was Babe Ruth who hit 54 home runs in 1920.