Ambrozic was born near Gabrje in the Kingdom of Yugoslavia (modern-day Slovenia) as Alojzij Matej Ambrožič, one of seven children of Alojzij (or "Lojze") Ambrožič and Helena Pečar. In May 1945, he and his family fled to Austria, after which he completed high school in Ljubljana and various refugee camps (Vetrinj, Peggez and Spittal an der Drau). The family went to Canada in September 1948, where he studied at St. Augustine's Seminary and was ordained a priest in Toronto on 4 June 1955. He served first in Port Colborne, Ontario, and later taught at St. Augustine's Seminary in Toronto.