Close but not quite true, from a bio of him:
Born Max Faktor in Lodz, Poland during the 1870s, at the age of eight Max was placed in apprenticeship to a dentist-pharmacist. Years of mixing potions instilled in him a fascination with the human form. Factor opened his own shop in a suburb of Moscow, selling hand-made rouges, creams, fragrances, and wigs. A traveling theatrical troupe wore Factor’s make-up while performing for Russian nobility, and the door to fame and fortune opened wide. The Russian nobility appointed Factor the official cosmetic expert for the royal family and the Imperial Russian Grand Opera.
In 1904, Factor and his family came to America. He had a fresh start in St. Louis at the 1904 World’s Fair, selling his rouges and creams, and operating under the name given to him at Ellis Island, Max Factor.