Matt was born in Katerini, Greece, in 1936. In 1942, he went into hiding with the Nazi occupation of Greece. The Yosafats hid in places including a cave and tobacco shelter, rarely safe and often separated. Ultimately, the Yosafat family reunited in Katerini and were liberated, but the outbreak of a civil war led the family to emigrate to the United States in 1951. In 1955, Matt met his wife, Anneliese — who had arrived in the United States with her family shortly after the war — and they were soon married in 1959.