Andrei is the son of former professional footballer Sergey Gotsmanov, a four-time Belarusian Footballer of the Year who played for the Soviet Union at the 1988 UEFA European Football Championship. He was born in Minsk, then part of the Soviet Union, but came to the United States with his family in 1996 when his father signed to play for Minnesota Thunder. He also has an older brother, Sasha, who played for the Colorado Rapids and the former professional club Minnesota Thunder.