I have a character in a book I wish to write in the first person; however, one of the main characters who narrate lives in China. He speaks only Cantonese and Mandarin, so it's a problem, but it is important they only speak these languages and live in China. What should I do?
I see no reason you would do anything differently than if you were writing about an English-speaking character.
I'm English. I can't speak any language other than English. But as a massive anime nerd, I have several stories - including one in first-person - that take place in Japan, with Japanese-speaking characters. They are written entirely in English, but I do use Japanese words that don't have English equivalents, as well as Japanese honorifics like -san and -chan. These help subtly remind readers that, even if the story is written in English, the characters aren't actually speaking English.
Think about it this way: surely you've read literature translated from another language? For example, Les Miserables, set in France. All characters speak French. Hugo doesn't need to tell you that they speak French, or that no character knows a word of English - the setting does that. You might be reading in English, but you know it's not really English the characters are speaking.
The way I usually think about it is this: the language the story is written in is transparent, "mother-tongue", "vanilla". Other languages are various flavours of "foreign", which I might be using in the story for various reasons. What happens when your in-story "foreign" is the language you're actually writing in (for example, your Chinese character comes to America)? You focus on how your POV character would see things. If he doesn't understand what's being said to him, you write "X said something I did not understand".
OP might be over complicating things. E.G. If narrator is Deaf, that doesn't preclude him from narrating, he may not understand what is being said by another but can still contribute as a narrator, at the very least his confusion. Try using a Stream of consciousness as used by Joyce or Irvine Welsh is a common literary medium. Are thoughts not universal in terms of language thus avoiding the problem (if there is one). Maybe my comparison to deafness is not valid. But it is based on personal experience. I have moderate to major hearing loss and schoolboy French in a Scot's accent, my visits to France are always fun ! Maybe a comedy in the making.