Rahme set an African junior record in April 2010, clearing 5.50 m (18 ft 1⁄2 in) at the South African Junior Championships.[8] He came close to his first senior medal later that season at the 2010 Commonwealth Games, where he was fourth behind Max Eaves.[9]
He struggled in his first years as a senior athlete, recording a best of 5.43 m (17 ft 9+3⁄4 in) in 2011 and declining to 5.20 m (17 ft 1⁄2 in) in 2012. After missing the 2013 season, he returned in good form the year after.[2] He ascended to the top the regional scene at the 2014 African Championships in Athletics, claiming the gold medal with a championship record of 5.41 m (17 ft 8+3⁄4 in).[10] He represented the continent at the 2014 IAAF Continental Cup, coming in sixth.[2]