Abrosimova was born in Leningrad, Russian SFSR, Soviet Union (today St. Petersburg, Russia), to Oleg and Ludmilla Abrosimov. Her father Oleg works as a welder in a shipyard and her older sister, Tatiana, was a professional ballroom dancer. While attending school she was trained for the then Soviet Olympic team. She was named the MVP of the 1996 European Basketball Championship (also known as "Eurobasket"), averaging 18 points, six rebounds and three assists per game. She was also a member of all-star teams that won the 1995 and 1996 European Championship.