Born in Chicago, Illinois, and raised there with a sister, Sally, and a father who died when Kweskin was 11, Kweskin learned to draw by copying Sunday newspaper comics, particularly those of Hal Foster, on sheets of grocery wrapping paper. Per differing accounts, he either won a scholarship at 16 to the Studio School of Art, and the following summer enrolled in a course at the Chicago Academy of Fine Arts, or before his senior year of high school won a scholarship to a summer course at the Academy. By both accounts one classmate was the future celebrated military cartoonist Bill Mauldin. At 16, through a neighbor who worked with Foster's brother, Kweskin visited Foster at the respected writer-illustrator's Evanston, Illinois, attic studio and subsequently "wrote a story about my visit for my high school newspaper." After high school, Kweskin worked as a night-shift copyboy for "Chicago Tribune" newspaper, and then entered the U.S. Army.