It’s actually kinda the premise of this old Chinese drama from like the 90s. It’s called the Plum Blossom Birthmark. This woman gives birth to a girl but decides to give her up because the show takes place in old times and she felt her position was threatened because her husband had taken on a concubine so she decides to swap out her baby girl for a boy. She brands the girl with a plum blossom mark on her back so that she can maybe find her later. Years later the little girl and boy grow up and fall in love.