Robb was born in Denver, Colorado, the daughter of Janet, an interior designer, and David Robb, an architect. She was named after her maternal great-grandmother, Anna Sophie, and her paternal grandmother, Anna Marie. Robb is of Danish, English, Irish, Scottish, and Swedish descent. She grew up in a Christian home and was home-schooled. She started taking an interest in acting and began by performing in front of 500 individuals on her church stage. She competed in dance and gymnastics for four and a half years, but quit in order to focus on acting. In 2009, the "Arapahoe Herald" reported that she was attending Arapahoe High School in Centennial, Colorado. She graduated in 2012.