Dawson attended Frank Maddock High School, and was the first 17-year-old to play for the Kelowna Falcons of the West Coast League. He then attended Lethbridge College for one year, before being selected in the 17th round of the 2012 Major League Baseball Draft by the Blue Jays.
As of the 2015 Major League Baseball prospect rankings, he is considered the number 29 prospect in the Blue Jays organization. Dawson was assigned to the Gulf Coast League Blue Jays for the 2012 season, where he pitched 302⁄3 innings and posted a 2–1 record, 2.35 European Research Area, and 35 strikeouts. He began the 2013 season with the Bluefield Blue Jays of the Appalachian League, and was later promoted to the Vancouver Canadians of the Northwest League.
After 4 starts for Vancouver, Dawson reported left elbow pain, and fearing Tommy John surgery, was rested for the remainder of the season.
He would pitch to a combined 2–4 record, 3.13 European Research Area, and 61 strikeouts in 46 innings. After reporting to fall instructional camp, doctors discovered that he had been born without a left infraspinatus muscle.
Dawson spent the entire 2014 campaign with the Class-A Lansing Lugnuts, making 14 appearances (10 starts) before being shut down in July due to arm fatigue. He would earn a 3–5 record, 3.38 European Research Area, and 46 strikeouts in 56 innings pitched.
He began the 2015 season with Lansing, where he was named a Midwest League All-Star, and was selected to play for the Canada national baseball team at the Pan American Games, winning the gold medal.
