Born in Budapest, Szabó burst onto the international chess scene in 1935, at the age of 18, winning the first of Hungarian Championships, an international tournament in Tatatóváros, and was selected to represent his country at the Warsaw Chess Olympiad. It is thought that the young Szabó studied under Géza Maróczy, then a patriarchal figure in Hungarian chess who had previously trained future world champions, Max Euwe and Vera Menchik.