2010-11: Josh Wesley skated for the East Coast Eagles program in North Carolina.
2011-12: Wesley played for the Carolina Junior Hurricanes U16 AAA team. He scored 7 goals with 6 assists and 10 penalty minutes in 18 regular season games and scored 1 goal with 6 assists and 14 penalty minutes in five playoff games. Wesley was invited to USA Hockey's 2011 National Team Development Program Evaluation Camp in March and was offered a spot in the program for the 2012-13 season. He was selected by Plymouth in the fifth round (101st overall) in the 2012 OHL Priority Draft.
2012-13: Wesley moved to Ann Arbor to skate for the NTDP's U17 team and played for the USA's bronze medal team at the 2013 World Hockey Challenge in Canada. He had 7 assists and 20 penalty minutes in 56 regular season games and had 2 assists with 4 penalty minutes in six games at the WHC.
2013-14: Wesley joined the OHL's Plymouth Whalers — skating in 66 of 68 regular season games as a 17-year-old rookie. He scored 2 goals with 6 assists and was -2 with 62 penalty minutes. Plymouth reached the playoffs; finishing fourth in the West Division. Wesley was ranked 79th amongst North American skaters in Central Scouting's mid-term rankings prior to the 2014 NHL Draft.