Kulboka played in the youth ranks of Žalgiris Kaunas, with the club's reserve team of Žalgiris-2 Kaunas, until he signed a five-year deal with German powerhouse Brose Bamberg, in August 2015. In his first year, he exclusively saw action on their affiliated teams in the German under-19 youth Bundesliga NBBL, and in the second German division 2. Bundesliga ProA. He helped Breitengüßbach capture the 2016 NBBL title, while averaging 6.4 points, as well as 1.5 rebounds a contest for Baunach in ProA play. In 2016, he attended the Basketball Without Borders Global Camp in Toronto, Canada, as well as the Adidas Eurocamp in Treviso. In the 2016–17 season, he improved his stats to 14.7 points, 4.3 rebounds and 2 assists per game for Baunach in ProA action. On 1 May 2017, Kulboka made his debut for Brose Bamberg in Germany's top-tier level Basketball Bundesliga, in a 61–74 win over Science City Jena, in which he recorded 13 points and 5 rebounds. In June 2017, Kulboka participated in adidas Eurocamp. He was named best sniper of the camp, by scoring 10 three-pointers in a row. Furthermore, he was also named to the First Team All-Eurocamp 2017. During the same year, Kulboka declared for the 2017 NBA draft, but he withdrew on 12 June. On 14 July 2017, he joined Orlandina Basket of the Italian top-tier level Serie A, on a loan. After averaging 10.3 points, 5 rebounds and 1.1 assists per game during the 2017–18 Basketball Champions League season, he was named the league's Best Young Player of the season. On 23 July 2018, Brose Bamberg announced, that Kulboka would return to the team. On 6 August 2019, Kulboka signed with Spanish club RETAbet Bilbao Basket. He averaged 8.5 points and 3.6 rebounds per game in his first season with the team. On June 12, 2020, he extended his contract for two seasons.
NBA
Near the end of the 2017–18 season, Kulboka would enter his name in the 2018 NBA draft, being one of only 11 international players to declare for the draft early that year. On 21 June 2018, he was drafted by the Charlotte Hornets, in the second round. He represented Hornets during the 2018 NBA Summer League. During his debut game he scored 12 points per 13 minutes and helped his team to achieve an 88–87 victory over the Oklahoma City Thunder. Kulboka represented Hornets during the 2019 NBA Summer League once again. He played his best game versus the China men's national basketball team, scoring 18 points and grabbing 4 rebounds.
