2009-10: Zach Pochiro played for the Nevada Stars in the North American Prospects Hockey League (NAPHL). He scored 18 goals with 11 assists in 20 games with 40 penalty minutes.
2010-11: Pochiro played for the Los Angeles Junior Kings U18 team. In 31 games he scored 22 goals with 12 assists. Pochiro was selected by Fargo in the sixth round (84th overall) of the 2011 USHL Entry Draft.
2011-12: Pochiro went to training camp with the WHL's Prince George Cougars before skating for Wichita Falls in the North American Hockey League. Pochiro led the Wildcats with 154 penalty minutes and and was the team's leading scorer with 18 goals with 16 assists in 52 games, finishing +8. Wichita Falls missed the playoffs after finishing sixth in the South Division.
2012-13: Pochiro returned to Prince George and made the Cougars as an 18-year-old free agent. He was the team's third-leading scorer, scoring 15 goals with 24 assists in 65 games, and was -4 with a team-leading 105 penalty minutes. The Cougars missed the playoffs after finishing fourth in the B.C. Division. Ranked 173rd amongst North American skaters in Central Scouting's final rankings, Pochiro was selected by St. Louis in the fourth round (112th overall) of the 2013 NHL Draft.