Puck was born in Sankt Veit an der Glan, Carinthia, Austria. He learned cooking from his mother, who was a pastry chef. He took the surname of his stepfather, Josef Puck, after his mother's remarriage. The marriage produced two younger sisters and a younger brother for Wolfgang. He trained as an apprentice under Raymond Thuilier at L'Oustau de Baumanière in Les Baux-de-Provence, at Hôtel de Paris in Monaco, and at Maxim's Paris before moving to the United States in 1973 at age 24. After two years at La Tour in Indianapolis, Puck moved to Los Angeles to become chef and part owner of Ma Maison restaurant.