Rau was born in Feuerbach, now a part of Stuttgart, in the German Kingdom of Württemberg, the son of a peasant who later became a factory worker. He grew up in the adjacent city of Zuffenhausen, now also a part of Stuttgart. After finishing school in spring 1913, he started work as a press operator in a shoe factory. In November 1913 he changed his employer and moved to the Bosch factory works in Feuerbach. There he completed his training as metal presser and remained until autumn 1920, with interruptions due to war service during 1917-1918 and the subsequent German Revolution of 1918–1919.