Melvin was born and raised in Saratoga, California. She became interested in acting at a young age through spending time at a local theater with her mother, who is a theater director. She made her first acting appearance as "Woodstock" in a local performance of You're a Good Man, Charlie Brown at the age of 5. She is a graduate of Independence High School in San Jose, California.
She trained at both the American Academy of Dramatic Arts in New York City, New York and the British American Drama Academy in Oxford, England.
Melvin is professionally trained as an actress, dancer, and singer, and also has martial arts training, at the level of a first degree blackbelt, in Taekwondo.