Egor Demin was born and grew up in Moscow, Russia, where he attended the Moscow Basketball Academy, where he trained until 2021. He received offers to play with other teams, including BC Khimki, but opted to stay at the academy until age 15 to be with his coach, Evgeny Gorbunov.
Demin sent highlight footage to European teams and had received six offers by 2021. He was considered a top Russian prospect and signed a six-year contract with Real Madrid in September 2021. Playing for the cadet "A" team in the Real Madrid academy, he helped them win the Spanish Cadet Championship in 2022 while averaging 17.3 points and 4.3 rebounds in the tournament. For the following two seasons, he was a member of the junior "A" team and the Real Madrid "B" team in the Liga EBA.
Following the 2023-2024 season, Demin opted to move to the U.S. to play college basketball. He committed to play for the BYU Cougars, where he was the program's first five-star recruit.