In international competitions debuted on September 25, 2005 in the FIS Cup competition in Bischofshofen. On January 14, 2006 scored the first points in the FIS Ski Jumping World Cup, taking 22nd place in the competition in Harrachov. On March 18, 2007 for the first time took part in Continental Cup, he was 26th in the competition in Zakopane. His individual best result in career is 9th place.
In individual competitions at FIS Nordic World Ski Championships 2013 took 31st place on the normal hill and 20th on the large hill. On March 2, 2013 he won there a bronze medal in team competition with teammates: Kamil Stoch, Maciej Kot, Piotr Żyła. Kubacki jumped 126 m and 128 m. The primary outcome of the competition his team took fourth place, but after re-counting the scores because of Thomas Morgenstern, who noticed a mistake in points and at the request of the Germans, they finished in third place (Norway was in front of the Polish, but Bardal's jump was badly counted).