Cave was signed as an undrafted free agent to a three-year entry level contract by the Boston Bruins on April 4, 2015. The native of Battleford, Saskatchewan, first played locally with Battleford in the Saskatchewan Midget AAA Hockey League from 2009 to 2011. After Cave was chosen by Kootenay with the No. 13 pick in the 2009 WHL Bantam Draft, his rights were traded to Swift Current on Jan. 9, 2011.
Cave, a center, was named captain of Swift Current in his third full season, when he finished with 70 points (33 goals, 37 assists) in 72 games. However, Cave was not selected in the 2014 NHL Draft. He returned to Swift Current the following season and had a WHL career-high 75 points (35 goals, 40 assists).