Marsh was born in Brecon, Wales, but moved to Blackborough, near Cullompton, Devon aged eighteen months. Aged 17, she began studying with the renowned singing Teacher April Cantelo, with whom she still has lessons. Marsh graduated with a First-class Honours degree from Birmingham University and was awarded the Barber Scholarship to study Opera at the Royal College of Music. In 1999 she won the MOCSA (Morriston Orpheus Choir Supporters' Association) Young Welsh Singer of the Year, whose previous winners have included Bryn Terfel and Anthony Stuart Lloyd.