Zniszczoł, who jumps for the WSS Wisła , appeared for the first time at the FIS Cup jumping in 2007 internationally, without being able to achieve top placings there. In the 2010/11 season he was used for the first time in the Continental Cup. He celebrated his international breakthrough in the summer series of the Continental Cup one year later: With a win in Trondheim , second places in Stams and Trondheim and six other top ten placements, he won the 2011 Continental Cup summer ranking. As he was also on snow continued to achieve good placements in the Continental Cup, e.g. B. with a second place on December 13, 2011 in Almaty , Kazakhstan , was used in the Four Hills Tournament 2011/12 for the first time in the World Cup and was able to qualify for the main field at the jumping in Oberstdorf and Garmisch-Partenkirchen , where he was 48th only came third from bottom. Zniszczoł was then used again at the Wielka Krokiew in Zakopane and was not only able to achieve his first World Cup points on January 20, 2012, but also jumped into the top ten with ninth place. One day later he again achieved a good placement with 14th place on the same hill. On March 3, 2012, Zniszczoł was used for the first time in the Polish team at the team world cup competition in Lahti, Finland , and was able to secure third place and thus his first World Cup podium with her.
At the European Youth Olympic Festival 2011 in Liberec , Zniszczoł won the gold medal in the team competition with the Polish team. Two years later, he started at the Winter Olympics for the first time and won the team competition there with the Polish team. He finished the individual competitions as eighth (large hill) and tenth (normal hill).
After Zniszczoł won the silver medal at the 2012 Junior World Championships in Erzurum, Turkey, both individually and with the Polish team, which also included Tomasz Byrt , Bartłomiej Kłusek and Klemens Murańka , he succeeded a year later with the team, to which this time Kłusek, Murańka and Krzysztof Biegun belonged to him, although the defense of the silver rank, but in the individual he fell back to ninth place. In 2014 he was only 13th in the Italian Fiemme Valley , but was able to win the title with the team, which this time also included Murańka, Biegun and Jakub Wolny .