Pupuma was born and grew up in Johannesburg. He attended St Benedict's College in Bedfordview, matriculating in 2011 alongside fellow future professional rugby player, Luther Obi. After school, Pupuma studied at the University of the Witwatersrand, and he also played rugby for their senior team in the Varsity Cup in 2013, 2014 and 2017 and in the Varsity Shield in 2015 and 2016. He came into a team that were promoted as champions from the Varsity Shield in 2012 to make their Varsity Cup debut in 2013. However, his team found the going tough at the higher level, losing all their matches in 2013 and 2014 to be relegated back to the second-tier competition for 2015. Pupuma scored four tries in the competition to help his team to the final of the competition, where they lost to, and five tries in their 2016 campaign, as his team went one better, beating 39–2 in the final to win promotion back to the Varsity Cup for 2017. He had a stand-out season in that competition, helping Wits to their best-ever finish of fifth, and being named in the Varsity Cup Dream Team at the conclusion of the series, appearing as a replacement in their 19–50 defeat to the South Africa Under-20 team.
Pupuma made his first class debut on 7 May 2016, coming on as a 30th-minute replacement in the 's Currie Cup qualification match against in Randburg. He made one more appearance in the competition, also as a replacement against in their match against. He made four appearances for the Golden Lions XV in the 2017 Rugby Challenge, including his first start in first class rugby in their 84–0 victory over Namibian side the. He was also included in their squad for the 2017 Currie Cup Premier Division, but failed to make any appearances in the competition.
Pupuma was included in the Southern Kings squad for their inaugural season in the Pro14 competition. He made his debut for the Kings in a 10–57 defeat to Welsh side Scarlets in their opening match of the competition, coming on as a second-half replacement, and again appeared as a replacement in their second match, scoring a late try in a 10–32 defeat to Connacht in Galway.
