Baer was born on February 11, 1909, in Omaha, Nebraska to Jacob Baer (1875–1938), who was half Lutheran German and half German Jewish, and Dora Bales (1877–1938), who was of Scots-Irish Protestant American ancestry. Baer was raised in a nominally nonsectarian home. His elder sister was Frances May Baer (1905–1991), his younger sister was Bernice Jeanette Baer (1911–1987), his younger brother was boxer-turned-actor Jacob Henry Baer, better known as Buddy Baer (1915–1986), and his adopted brother was August "Augie" Baer.
Move to California
In May 1922, tired of the Durango, Colorado winters, which aggravated Frances's rheumatic fever and Jacob's high blood pressure, the Baers drove to the milder climes of the West Coast, where Dora's sister lived in Alameda, California. Jacob's expertise in the butcher business led to numerous job offers around the San Francisco Bay Area. While living in Hayward, Max took his first job as a delivery boy for John Lee Wilbur. Wilbur ran a grocery store and bought meat from Jacob.
The Baers lived in the Northern Californian towns of Hayward, San Leandro and Galt before moving to Livermore in 1926. Livermore was cowboy country, surrounded by tens of thousands of acres of rangeland which supported large cattle herds that provided fresh meat to the local area. In 1928, Jacob leased the Twin Oaks Ranch in Murray Township, where he raised more than 2,000 hogs and worked with daughter Frances's husband, Louis Santucci. Baer often credited working as a butcher boy, carrying heavy carcasses of meat, stunning cattle with one blow, and working at a gravel pit, for developing his powerful shoulders (an article in the January 1939 edition of The Family Circle Magazine reported that Baer also took the Charles Atlas exercise course.)