Barkley was born in Laredo, Webb County, Texas to Joseph S. Barkley and the former Antonia Cantu. Joseph was a career Soldier, and the couple married in Starr County, TX while Joseph was stationed at Ft Ringgold, TX. Deployed to Puerto Rico shortly after David's birth, the family remained in Texas. David grew up with his Mexican-American mother and younger sister while his father remained in the Army. David first enlisted in the Texas National Guard, entering the U.S. Army in April 1917, shortly after the U.S. entered World War I. He enlisted under his legal name, though some claim he used his Anglo father's name only to avoid being segregated into a non-combat unit. Segregated units, however, not only applied to African Americans in the Army at that time but also to Hispanics according to U.S. Army regulations. It was not until May 1917 when an Act of Congress passed to increase needed manpower to allow Hispanics to join in the fight.