Mušič's father was mobilized and served on various battlefields during the First World War. In 1915, during the Battles of the Isonzo, the family (his mother with two children) was forced to flee to Arnače, a village near Velenje in the Duchy of Styria, where Zoran attended elementary school. In the spring of 1918, toward the end of World War I, the family moved back to Gorizia, but they were expelled again in late August 1919 by the Italian authorities, which had occupied the region. They moved to Griffen in Carinthia, but were expelled once again by the Austrian authorities after the Carinthian Plebiscite in late October 1920. They finally settled in Lower Styria, then part of the Kingdom of Serbs, Croats and Slovenes.