Levavi was born the youngest of three sons to a wealthy Russian Jewish family of good standing in the community and a lineage connected directly to the famous Rabbi "The Vilnius Gaon" in Vilnius, Lithuania in 1912. Levavi's mother fled with him and his brother to Danzig on the eve of the Russian revolution. Orphaned of both parents Levavi's education and were taken care of by his older brother Fima Leibman. He completed his studies in philosophy, mathematics and physics at the universities of Heidelberg and Danzig in 1930. After graduating he emigrated from Germany to Palestine, where in 1932 he received his Master of Arts in Philosophy, at the Hebrew University of Jerusalem.
He worked as a contributing writer for the daily newspaper Davar in Palestine, until he was sent to Germany on a mission on behalf of the HeHalutz Movement (1936–1938). When he came back to Palestine in 1938 he became involved in integrating and coordinating various Zionist and political movements until the formation of the state of Israel.