Born in Obrigheim, then in the Kingdom of Bavaria, now Rhineland-Palatinate, Germany, Alexander emigrated to the United States in 1867 and settled in New York City. Within a year, he accepted an invitation from his cousin in Missouri to work in a clothing store in Chillicothe, where he showed a talent for the business and was made a partner in the store in 1874. In 1876, Alexander married Helena (née Hedwig) Kaestner (1853–1949), a Christian immigrant from Germany who converted to Judaism. Together, they had a daughter, Leha Alexander Spiro (1885–1979).