Alvheim was born in Øygarden, Hordaland, to fisherman and farmer Joakim Knutsen Alvheim (1893–1958) and housewife Ingeborg Larsen (1895–1972). From 1954 to 1956 he worked in the Norwegian Navy as a Medical Quartermaster, and finished his education as a nurse anesthetist. After working some years in Norway at "Askim sykehus", from 1958 to 1961 he worked as head nurse at the United Nations Interim Force in Lebanon, and later returned to work in Norway at "Notodden sykehus". After that he did several missions as an aid worker, for the Norwegian Church Aid in Bangladesh in 1972 and Ethiopia in 1974, and for the Red Cross in Lebanon in 1976.