During the 1954 FIFA World Cup, Kubsch almost became the starter of the German team. The standard goalkeeper Toni Turek had shown some weaknesses in the first game against Turkey and the second goalkeeper Heinrich Kwiatkowski had conceded eight goals in the game against Hungary, which made Sepp Herberger consider giving Kubsch a chance in the second game against Turkey.
During the 1954 FIFA World Cup, Kubsch was almost selected as Germany's starting goalkeeper due to Toni Turek's performance and Heinrich Kwiatkowski's poor showing.