Born in Malmö, Sweden, Malja began his karting career in Formula Micro in 2006, winning the Gunnar Nilsson Memorial trophy the following year.

[4] In 2011, Malja graduated to single-seaters, racing in the ADAC Formel Masters championship in Germany, despite being just 15 years of age.

[6] He continued with the team for a second season in 2012, taking three race wins and a further thirteen podium places to finish runner–up to champion Marvin Kirchhöfer.

[8] In the NEC championship, he contested eight races, taking podium places at the Nürburgring and Most to finish fifteenth in the standings.

[16] In May 2015, Malja took part in the Pau round of the FIA European Formula 3 Championship, racing for EuroInternational in the car originally intended for Marvin Kirchhöfer before he left the team prior to the start of the season.