Born in Sudan,[2][3][4] Kuol grew up in a small village next to a military base that backed on to the jungle.

[5] He and his family also spent time living at Kakuma, the world's biggest refugee camp located in Kenya.

[6] He moved to Australia in 2006 when he was nine years old,[2][3][4] when his uncle, mother, three brothers and two sisters fled from war-torn South Sudan.

He also led the Australian Capital Territory (ACT) team to a fifth-place finish at the U20 National Championships, averaging 15.6 points and 8.1 rebounds per game.

[3][4] Kuol debuted in the South East Australian Basketball League (SEABL) for the Canberra Gunners in 2015, averaging 6.0 points and 1.6 rebounds in 18 games.

He scored in double digits 17 times in his 20 regular-season games with four 20-point outings and was subsequently named third-team All-Horizon League.

[19] He entered the 2021–22 season having been told he was not guaranteed to be part of the rotation or receive any minutes, but due to numerous injuries to his back-court teammates, he was thrust into the line-up and quickly became one of the Taipans' most important players thanks to his defensive intensity and energy.

[20] On 5 February 2022, he scored 26 points with eight 3-pointers in a 102–94 win over the Brisbane Bullets,[21] becoming just the third player in Taipans history to record eight 3-pointers in a game.

[27][28] In 2022, Kuol was selected to play for the South Sudanese national team in the FIBA World Cup Qualifiers.