This exact thing has happened many many times in history. Not someone transported through time, but someone travelling to a place where nobody (or virtually nobody) speaks the same language, or even one related to yours.

I mean, for the extremely obvious examples, before the Columbian exchange, nobody in the Old World (Eurasia/Africa) had ever encountered any New World (Americas) language and vice versa. They managed to learn how to communicate within a fairly short time period.

But this was just the most obvious example. Until relatively recently (like past half millennia, or so), it was common enough.

You’d learn through immersion. You hear the language every day all day. You try to communicate by pointing and gesturing. Pretty soon you start picking up individual words (point at a piece of bread and say ‘bread’ over and over. Someone is going to respond with their word for bread. Do that a few times and you’ll learn the word for bread, etc, etc). That builds into common phrases. Before too long, you’re able to hold very rudimentary conversations, and it just builds from there.