Incrocci was born in Brescia, into a family including several actors, such as his sister Zoe, and spent his youth moving with them to numerous places of Italy. His first work in the cinema world was a dubber for Mario Monicelli's first movie, I ragazzi della Via Paal (1935). Subsequently, he worked for a radio, and in the meantime he started writing comic scripts. He also studied law, but without graduating.
He spent the first four years of World War II in France, as a prisoner of the French Army first and, later, of the Wehrmacht. He managed to escape, however, and fought for a year with the United States Army. Back from the front, he worked again in the radio and for wrote for theatre and humour magazine.