Van Assche won the 2021 French Open Boys' Singles title, defeating fellow countryman Arthur Fils in the final.

445, Van Assche received a wildcard for the qualifying event at the 2022 Open Sud de France but lost to Roman Safiullin.

In December, Van Assche won his maiden Challenger title in Maia defeating qualifier Maximilian Neuchrist in the final.

[10][11] Van Assche received a wildcard into the 2023 Australian Open main draw to make his Grand Slam tournament debut in singles,[12] losing in the first round to 11th seed Cameron Norrie.

[16][17] The following week he recorded his first ATP win at the Estoril Open over qualifier Pedro Sousa[18] after entering into the main draw directly.

[19] Van Assche recorded his first top-100 win over Stan Wawrinka at the Srpska Open,[20] before losing to world No.1 Novak Djokovic in the second round.

[25] In November, he qualified for the Next Generation ATP Finals[26][27] where wins over Abedallah Shelbayh[28] and Alex Michelsen[29] were enough for Van Assche to advance from his group into the semifinals despite a defeat to Hamad Medjedovic.