Max Speter was born in Beszterce, Austria-Hungary (now Bistrița, Romania), the youngest of seven children, to his Jewish parents Johann Speter and Anna Dollberg. He grew up in Bistrița and graduated in 1900 from the city's German Gymnasium.
Speter began studying engineering at the Budapest University of Technology and Economics. He then moved to Hanover, and completed his studies in Munich where he received his Diploma in Mechanical Engineering. After graduating he worked with Oskar von Miller, founder of the Deutsches Museum, as a member of the museum's founding team. For a while he worked in the chemical industry in Germany and Hungary. Then he was hired as a researcher at the Humboldt University of Berlin, where he also started his Ph.D. thesis. His doctoral advisors were Hans Heinrich Landolt and Walther Nernst, who later won the 1920 Nobel Prize in chemistry. Speter acquired his doctorate in 1910.