Born in St. Louis, Missouri, Schmidt signed with the New York Giants in 1951, and rose methodically through their minor league system.

He missed the 1953 and 1954 seasons due to military service, but when he returned to baseball he was selected all-star catcher in successive years in the Double-A Texas League (1956) and the Triple-A American Association (1957).

Concurrently the Giants' catchers of the 1950s, Wes Westrum, Ray Katt and Valmy Thomas, were aging or proving ineffective, and the franchise itself transferred to San Francisco.

As a rookie with the 1958 San Francisco Giants, Schmidt was selected to be on the National League team in the 1958 All-Star Game.

[1] He holds the Major League record for most putouts in an extra inning game with 22, set on June 22, 1958.