Treasurethe Moment is the third and final foal of Draconic Treasure (Street Cry), a winner in North America who died in 2022. Her older sister Kind Treasure (Frankel) is in foal to Alabama Express. Draconic Treasure is a half-sister to three winners and to the unraced Hazy Morning (Curlin), dam of Bella Mia (Yazamaan), a Listed winner in Peru.

Second dam Hazy Glow (Invincible Spirit) won at Dundalk as a 2-year-old. She is a half-sister to Rich Tapestry (Holy Roman Emperor), who won stakes races in the United States, Dubai and Hong Kong, among them the Listed Sprint Cup in Hong Kong.

Third dam Genuine Charm (Sadler's Wells) is a full-sister to the Group 1 winner and sire Refuse To Bend (Sadler's Wells) and a half-sister to Media Puzzle (Theatrical), winner of the Gr.1 Melbourne Cup.