Born in Wisconsin Rapids, Wisconsin, Natwick studied at the School of the Art Institute of Chicago and had five brothers and two sisters. Natwick's parents, James and Henrietta (Lyon), owned a furniture store. His grandfather, Ole, was one of the earliest Norwegian immigrants to the United States arriving in Wisconsin in 1847 (Ole was born on April 8, 1826, to Ole Torkjellson Natvig and Anna at Sagi Natvig, Ardal, Sogn, Norway). He had eleven children in Grand Rapids, Wisconsin (now part of Wisconsin Rapids), including James W., Grim's father, and Joseph, who was the father of Mildred Natwick, Grim's first cousin.