Biliński's racing career started in 2018, when he raced in the Winter Series of the Ginetta Junior Championship. He then competed in the first seven rounds of the 2019 season with Alastair Rushforth Motorsport. His first victory and pole position would come at the first race at Donington Park.
The Pole went on to finish two more races in third position and finished eighth in the championship at the end of the year.
2021
For the 2021 campaign Biliński switched to Carlin to race alongside Kai Askey, Tasanapol Inthraphuvasak and Dougie Bolger.[4] Biliński only did a part season in the British F4 Championship, Biliński scored his first podium finish of the season at Oulton Park in race 3.
GB3 Championship
Biliński moved into the GB3 Championship to replace Frederick Lubin, who had fallen ill, at Arden International.[5] The Pole experienced a very strong debut weekend, with three finishes in the top five with only 1 day of testing.[6] His next weekend would be even more successful: after finishing third in the first race, Biliński became the first Polish driver to win a race in British F3.[7]Snetterton was up next, and there Biliński showed blistering pace, finishing third in the first and second race, and then won race 3 on Sunday, becoming the only driver to score a podium at every race on the same weekend that year. [8] The Pole won another race at Oulton Park and ended his season in seventh in the standings, beating both of his teammates with only a part season.
Formula Regional
2022
For 2022, Biliński moved up to the Formula Regional European Championship for the 2022 season with Trident. He had two points finishes in the season, with one being his maiden podium in the series at the first race of the Hungaroring, he finished the championship in 18th with 17 points.
2023
Biliński was retained by Trident for the 2023 season.[9] He scored 23 points and finished 21st in the championship standings.
For his main campaign, Biliński remained with Trident for a third straight season in the 2024 Formula Regional European Championship.[12] He achieved his first pole in the series in Spa-Francorchamps and he would later finish in second, giving him his first podium of his campaign.[13] Unfortunately for Biliński, he was hospitalised in a road accident just before the Zandvoort round and was forced to withdraw from the event.[14] Biliński later revealed he had undergone surgery to fix two broken vertebrae from the road accident, forcing him to step away from racing for the time being.[15]