Central Coast Mariners Kuol began his senior career with Victorian side
Goulburn Valley Suns, after coming through the side's youth teams. Kuol trialled with
A-League clubs
Melbourne Victory and
Western United but was unsuccessful in receiving a contract. Kuol also briefly trialed with Portuguese club
Sporting CP in their under-19 squad. Three days later, Kuol was awarded a scholarship with the Mariners, extending to the end of the
2020–21 season. He made his starting debut for the Mariners in a goalless draw against
Newcastle Jets on 24 July 2020, and received media attention for his colourful post-match interview.
VfB Stuttgart On 16 April 2021, following interest from several top European teams, Kuol signed a 4-year contract with
VfB Stuttgart, signing until June 2025. Delegated to
VfB Stuttgart II, Kuol scored seven goals in his first 13 appearances with the reserve side, leading second in the goalscoring charts for the
Regionalliga Südwest by November. On 31 January 2022, Kuol was loaned to
SV Sandhausen until the end of the season. He made his debut on 30 April 2022 in a 2–1 defeat to
Schalke, in which he was
sent off in the 5th-minute of added time, after a challenge on
Thomas Ouwejan. Kuol was suspended for three games, missing the remaining matches of the league season. On his return to Stuttgart, Kuol made his
Bundesliga debut on 27 January 2023 in a 2–1 defeat to
RB Leipzig.
Return to Central Coast Mariners On 10 July 2023, Kuol signed a three-year deal to return with Central Coast Mariners. He made his returning debut in the A-League on 20 October 2023 in a 3–0 loss against
Adelaide United at
Coopers Stadium. Kuol was taken off in the 34th minute of the match after suffering a knee injury from a challenge on
Alexandar Popovic; doctors tested for an
ACL injury but concluded it to be a knock. Kuol was part of the Mariners' Championship, Premiership and
AFC Cup winning
2023-24 season. Kuol scored the only goal of the
2024 AFC Cup final in the 84th minute against
Al Ahed. At the end of the
2024-25 season, Kuol left the Mariners. ==International career==