Her father was known as a freethinker. He sponsored Russian avante-garde artists and their projects through his enthusiasm for artistry. Geva described her mother, Tamara Urthal, as a beautiful but selfish woman. Her parents were unable to marry until their daughter was six years old. As a child, she lived in a huge 19th-century house (Ivan Zheverzheev′s house at Rubinstein Street, 18) which had an extensive art, book and theater collection as well as a miniature theater all organized by her father and his years of collecting such artifacts. Her father had agents all over who found art, writings, and artifacts from a variety of well-known artists to add to his massive collection. Geva has said that this collection was her father's most prized possession. After the Russian Revolution ended and Levko had passed away, his extensive theatre memorabelia collection was preserved and put into an exhibit at . Geva grew up in the midst of the Bolshevik Revolution where she experienced true hardships in her youth.