Pytlick began playing handball in the youth ranks of
GOG Håndbold in 2012. He debuted in the
Danish Men's Handball League in 2019, playing six matches and scoring ten goals in his first season. Due to teammate Emil Lærke's injury, he gained more playing time in the 2019–20 season and won the Talent of the Year award. The following season, he won the Danish championship and was selected for the league's All-Star team. In 2022, Pytlick extended his contract with GOG but played only one more season, winning another Danish championship. In 2023, he signed with
SG Flensburg-Handewitt. In February 2025, he broke his right arm during a match against
Toulouse Handball in the
EHF European League. Despite the injury, he extended his contract with Flensburg until 2030 in April 2025. In December 2025 he announced his intention to join
Füchse Berlin in the summer of 2027. He cited his friendship with national team colleague
Mathias Gidsel as one of the primary reasons for the transfer. ==Achievements==