Born and bred in Krugersdorp, Steenkamp was eligible to represent the at youth level. He earned several call-ups to play for them at youth tournaments, from as early as primary school level; in 2006, he represented them at the Under-13 Craven Week tournament held in Oudtshoorn. He also played at the Under-16 Grant Khomo Week in 2009 and represented them at the Under-18 Craven Week – the premier high schoolrugby union competition in South Africa – in both 2010 and 2011. Steenkamp was also included in the 2011 South Africa Schools squad and he was named captain of the team that beat France 'A' 21–14 in Port Elizabeth. He then also made two appearances for the side in the 2011 Under-19 Provincial Championship.
After high school, Steenkamp moved across the Jukskei River to join the Pretoria-based prior to the 2012 season. He made eight appearances for the s in the 2012 Under-19 Provincial Championship and also captained the side. He scored two tries during the round-robin stage of the season in matches against and and doubled that tally by scoring a brace in their 46–35 victory over the in the semi-final of the competition. He also captained the side in the final, but ended on the losing side as ran out 22–19 winners. In 2013, Steenkamp was named captain of the South Africa Under-20 squad for the 2013 IRB Junior World Championship. He started all five matches for a South African side that won the competition in 2012 and attempted to retain the title in the 2013 event held in France. They started off in fine fashion, beating the United States 97–0 in the opening match. Steenkamp scored a try midway through the first half as South Africa ran in 16 tries. South Africa secured a 31–24 victory over England and a 26–19 victory over the hosts France to finish top of Pool A and qualify for the semi-finals. However, a 17–18 defeat by Wales eliminated the defending champions from the competition. They recovered in the third-place play-off match to beat New Zealand 41–34, with Steenkamp getting his second try of the tournament shortly after half-time. Steenkamp returned to domestic action after the tournament as he played for the s in the 2013 Under-21 Provincial Championship. Despite still being at Under-20 level, he also occasionally captained the side, including their 70–19 victory over where he started the match in an unfamiliar role of hooker. He made six appearances during the league stage of the competition and appeared as a replacement in both their 36–13 victory over in the semi-final and the final, where the Blue Bulls lost 23–30 to. He again represented and captained the side in the 2014 Under-21 Provincial Championship. He started eleven of their twelve matches in the competition, scoring a try in eight of those matches, including tries in consecutive matches against,, and. The Blue Bulls finished in second position on the log to qualify for the play-offs and Steenkamp captained them in their 23–19 semi-final victory over the and the final, where Steenkamp scored one of two late tries as the Blue Bulls won the final 20–10 to clinch the Under-21 championship. Steenkamp's nine tries during the season was the most by a Blue Bulls player during their victorious campaign. Steenkamp started the 2015 season by representing university side in the 2015 Varsity Cup competition. He appeared in their first two fixtures of the season and scored two tries in their 39–24 victory over defending champions. He suffered a posterior cruciate ligament injury that ruled him out for several months, but returned for the during the 2015 Currie Cup Premier Division season. He made his domestic first class debut on 25 September 2015, when he played off the bench in their 17–13 victory over the in Durban. He made an incident-filled home debut a week later, coming on as a replacement early in the second half, scoring his first senior try fifteen minutes after coming on, but also spending the final minutes of the match in the sin-bin following a 74th-minute yellow card. He also played off the bench in their final regular season match in a 25–24 win over the to help them finish second on the log and clinch a home semi-final for the first time since 2008.