Born in Buffalo, New York, Heim attended Amherst Central High School, where the cold weather limited how often he played outdoors.

The following year, the Athletics traded Heim to Texas, where he became the Rangers' starting catcher and went on to represent the team at the 2023 MLB All-Star Game.

[1] A childhood fan of the New York Yankees of Major League Baseball (MLB), Heim's favorite players were catchers like Jorge Posada and Russell Martin,[2] and he grew up watching the Buffalo Bisons, the Toronto Blue Jays' Triple-A affiliate, although they were part of the Cleveland Guardians organization at the time, play at Sahlen Field.

[5] The harsh climate in Buffalo meant that Heim could only play 20 outdoor baseball games in a season, and the team's stadium lacked an outfield wall, so home runs landed in nearby backyards or soccer fields.

[6] After batting .470 and picking off 12 baserunners during his junior year of high school, Heim was invited to play in several national exhibition games, where he caught the attention of professional scouts and college recruiters.

[12] Heim began the 2015 season with the Delmarva Shorebirds of the Single–A South Atlantic League, where he split time at catcher with Alex Murphy.

[13] He improved offensively to start the season, batting .258 with 10 extra-base hits and 16 RBI in 36 games before going on the injured list with a foot injury in May.

[18] Although he had a lifetime .216 batting average in 88 games for the Orioles organization,[19] Heim cited his time in Frederick as a turning point for his offensive development.

[20] On August 1, 2016, the Orioles traded Heim to the Tampa Bay Rays in exchange for veteran utility player Steve Pearce.

[12] Heim opened the 2017 season with the Low–A Bowling Green Hot Rods, where he batted .268 with nine home runs and 53 RBI in 77 games before being promoted back to the Stone Crabs in August.

[28] As a result, Heim was one of several Athletics prospects who began the pandemic-shortened season at an alternate training site as a member of the Oakland taxi squad.

[38] On February 6, 2021, Heim, Khris Davis, and Dane Acker were traded to the Texas Rangers in exchange for Elvis Andrus and Aramis Garcia.

[39] Heim hit his first major league home run on April 6, 2021, off Toronto Blue Jays pitcher Tommy Milone.