He did his secondary school studies at the Colegio Nacional del Montserrat in Córdoba and his university studies in law in the National University of Córdoba. In 1926, with the essay "The Epistemological Problem in Philosophy", Astrada won a scholarship to Germany. He studied at the universities of Cologne, Bonn, and Freiburg, under Max Scheler, Edmund Husserl, Martin Heidegger and Oscar Becker during his four years there.
When he returned to Argentina from Germany, Astrada was designated the head of Publications and Conferences in the Social Institute of the University of Litoral (1933-1934). There he began a vast career in distinct academic functions of the country: he was an adjunct professor of The History of Modern and Contemporary Philosophy in the School of Philosophy and Letter in the University of Buenos Aires (1936-1947); Professor of Ethics in the School of Science and Humanities in Education at the University of La Plata in La Plata (1937-1947); Professor of Philosophy in the Colegio Nacional de Buenos Aires (1939-1949); Professor of Nomology and Metaphysics in the School of Philosophy and Letters in the University of Buenos Aires (1947-1956); Director of the Institute of Philosophy in the University of Buenos Aires (1948-1956), etc.