How would I explain this within the story? What would be the cause of her not having vocal cords at such a young age? I've considered saying that she had laryngeal cancer as a child and had them removed. What are some other possible explanations I could use besides this?
i'm not sure you need to explain it - if you said your character was deaf from birth people would just accept it, being mute is no different
if your MC is mute since his birth, then you don't need to explain why. However, if you want to explore other options, try maybe he lost his vocals by accident or perhaps he was a singer and got them destroyed?
She wasn't mute since birth. She had vocal cords, but then lost them in some way during her childhood.
Do the vocal cords need to be completely gone, or could them simply being nonfunctional work for your purposes?
Hey, that's a good one. Parents pushed too hard? Vocal coach didn't know what they were doing? That's a whole novel's worth right there.
https://globalnews.ca/news/2355883/boy-born-without-vocal-cords-talks-with-voice-box-made-of-his-own-tissue/
That's another option to explore. Maybe his MC desired so much to be a singer, that her/his coach didn't know what to do, so in the process, the vocal cords are destroyed. At the same time, his dream is going down as well.
I think depending on the circumstances and age the character was when he/she lost them, it could affect characterization. So if you do want to 'from birth' they'd be used to it, if it's recent/tragic accident they may still be struggling to adjust, things like that. Laryngeal cancer sounds okay to me, but I am not a medical professional. As for explaining, I'd say you probably could get away with writing it in a way where it doesn't come up. Or if you did want to explain, a quick explanation would be best. Maybe someone expresses curiosity and your character explains, briefly. "I had laryngeal cancer as a child." Not much but still enough there. Unless it's about the trials and tribulations of being mute, I'd say don't focus in on that element too much.
You probably wouldn't...unless they know some form of sign language. Then you'd write it more or less the same as normal. Swap out "X said" dialogue tags with "X signed", and occasionally mention the way they signed to impart tone.
There is a movie on Netflix kind of like this, with a mute MC. In the movie, he had his vocal cords destroyed in an accident when he fell in the water and the propellors on a boat cut him. So maybe you could do something like that. Or, if they were born with it or something like that, then not much of an explanation is needed.
I knew someone whose larynx was crushed when she was hit by a car as a child. With a lot of therapy over a long time, she could eventually say some raspy words, but she learned to sign in the meantime and used a combination of the two.