Nikolayeva was born in Bezhitsa, in the Bryansk district, on May 4, 1924. Her mother was a professional pianist and studied at the Moscow Conservatory under the renowned pedagogue Alexander Goldenweiser, and her father was an amateur violinist and cellist. When in Leipzig the International Johann Sebastian Bach Competition was founded to mark the bicentenary of Bach's death in 1750, Nikolayeva won first prize in 1950. Dmitri Shostakovich, who was as a member of the jury, composed and dedicated the 24 Preludes and Fugues, Op. 87, to her: it remained an important part of her piano repertoire.