AFIK, Tana"ch rarely mentions the date of someone's death. Moshe death date is not mentioned in Tana"ch.
I gather that we infer this from the fact that he died exactly 120 years after he was born. I think this is directly inferred from a key word or phrase in a verse (don't recall which one.) Yet, we also don't know the date of his birth as that is not mentioned in Tana"ch, either. So how did Chachamim determine this?