Alford attended Petal High School, where he was the quarterback of the football team in addition to playing baseball. As a senior, he recorded 2,058 passing yards and 20 passing touchdowns, in addition to 1,731 rushing yards and 24 rushing touchdowns, and played in the U.S. Army All-American Bowl. In the same year, he batted .483 with four home runs and stole 14 bases in 14 attempts.

Alford was projected as a first-round talent going into the 2012 Major League Baseball draft, but made it clear that his intention was to continue playing football, leading many teams to pass over him due to signability concerns. The Toronto Blue Jays drafted Alford in the third round, 112th overall. He signed a contract with Toronto which paid him a $750,000 bonus and allowed him to attend university to play football, and then play baseball in the summer.

Alford made his professional baseball debut as a member of the Gulf Coast League Blue Jays in 2012 and played in five games, where he hit .167 with one home run and four stolen bases. Following the baseball season, he began attending the University of Southern Mississippi as a member of the football team, but transferred to the University of Mississippi after one year following an on-campus fight. Alford played six games in the Gulf Coast League in 2013, batting .227 with two RBI and two stolen bases. Due to NCAA transfer rules, he was not allowed to play football for the Ole Miss Rebels in 2013. The following year, Alford played nine games for the Bluefield Blue Jays of the Appalachian League and was then promoted to the Class-A Lansing Lugnuts for five games. In total, he batted .259 with two home runs, five RBI, and five stolen bases. He was relegated to a backup safety role for the Rebels in 2014, and made just six tackles in four games. On September 30, 2014, it was announced that Alford was leaving Ole Miss to join the Blue Jays organization full-time, and planning on attending their fall instructional league before playing in the Australian Baseball League. He would go on to play 36 games with the Canberra Cavalry, and batted .200 with three home runs, eight RBI, and seven stolen bases.

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