Baker grew up in Fort Walton Beach, Florida and attended Choctawhatchee High School, where he was a standout baseball and basketball player.

Baker was selected in the 40th round of the 2013 Major League Baseball Draft by the Pittsburgh Pirates, but opted not to sign.

[7] Baker was acquired by the Toronto Blue Jays on August 14, 2018, as the player to be named later to complete a trade for Seung-hwan Oh.

[8] Baker began the 2019 season with the Double-A New Hampshire Fisher Cats before being promoted to the Triple-A Buffalo Bisons, where he had a 3.68 ERA and 31 strikeouts in 22 innings pitched.

[9] Baker did not play in a game in 2020 due to the cancellation of the minor league season because of the COVID-19 pandemic, but was assigned to the Blue Jays' Alternate Training Site.

[1] On the final day of the season, Baker pitched a scoreless ninth inning in the first game of a doubleheader against the Blue Jays to earn his first career save.