Olsen started his youth career at Alsønderup SG&I and joined the FC Nordsjælland academy in 2012. He later made his professional debut for the same club. In 18/19, he scored 32 goals for the Danish top club, which earned him a transfer to the Italian Serie A side, Bologna. After two and a half years at Bologna, Olsen made the move to Club Brugge. He signed a four-year contract, lasting until 2026.
Keen followers of the Belgian national team may already be familiar with Olsen from the UEFA Euro 2020 tournament. He featured in the group stage match against Belgium. He also earned playing minutes in the same tournament against Finland