Позавчера (pozavchyera) in Russian. Pretty sure French has something as well.

Usually you do just say “the day before yesterday/last”, and it’s super awkward. Nothing else is guaranteed to be understood (people are being creative with new words in this thread). It’s the same for “the day after tomorrow”. Two days ago might also work, but that could mean different things, depending on if you’re counting the present day or not.