Kacper Oeleszuk took part in international javelin competitions for the first time at the U18 World Championships in Lille. In the qualification he reached 65.85 m with the 700 gram javelin and was eliminated as eighth in his qualifying group, overall he finished 14th. In June 2012, now starting in the U20 age group, he won the Polish Junior Championships. A month later he entered the U20 World Championships in Barcelona, where he finished 37th with a width of 62.93 m. In 2013 he increased his best distance by more than four meters. At the U20 European Championships in Rieti, he moved into the final, in which he threw the fourth largest distance with 73.24 m.
In 2014 he increased his personal best to more than 77 meters. At the Polish championships he was seventh. His greatest sporting success so far was the victory at the U23 European Championships in Tallinn. His final width of 82.29 m is still his best performance today (as of 2020). In September, Oleszczuk was also the Polish U23 champion. In 2016 he made it into the final of the European Championships in Amsterdam, where he finished eighth with 79.34 m. In the following seasons he could no longer build on the performances he had already shown.