2010-11: Brycen Martin appeared in his first midget AAA game as a 14-year-old — playing one game with the CBHA Rangers in Alberta — and played for the Calgary Bisons bantam AAA team. Martin also played for the Calgary South Flames in the Alberta Cup – scoring 1 goal with 3 assists and 4 penalty minutes in five games. He was the second player taken in the 2011 WHL Bantam Draft when he was taken by Swift Current in the first round.
2011-12: Martin made his WHL debut with Swift Current and played for the Calgary Buffaloes midget AAA team after playing for Team Alberta in the 2011 Western Canada U16 Challenge Cup. He had no points nor penalty minutes and was -3 in three games with the Broncos. Martin scored 6 goals with 11 assists and had 65 penalty minutes in 25 midget games with the Buffaloes. He had 1 goal for Team Alberta, which captured the gold medal. Martin also represented Canada for the first time: participating in the European Youth Olympics. He had 5 assists and was +4 in six games.
2012-13: Martin skated in 67 of 72 regular season games for Swift Current in his first full WHL season and played for Canada Pacific in the 2013 U17 World Hockey Challenge. He scored 2 goals with 17 assists and was +3 with 32 penalty minutes as the Broncos finished third in the East Division. He had no points nor penalty minutes and was -5 in the five game playoff series with Calgary. Martin led all tournament defensemen with nine points (2 goals, 7 assists) in five games at the WHC playing for Canada Pacific.
2013-14: Martin attended Hockey Canada's U18 summer camp before returning to Swift Current for his second season with the Broncos.