So far, I haven’t seen anyone suggest using sign languages. The earliest mention of them is by Socrates (through Plato) in the fifth century BCE, so depending on your definition of “primitive”, I’d say it’s quite likely that some kind of sign language exists in the region of any hypothetical story’s setting.
Sign languages are natural languages just as much as spoken languages, so if there exists a community of people who cannot hear and/or speak, a sign language will evolve over time through which they express themselves. As such, a mute protagonist could certainly sign instead of speaking. The story setting could accommodate this by having all or most of the other characters be profficient in the language too, and any signed dialogue would then appear in italics. Alternatively, the MC could have a translator on hand (also somehow justified by the story), which would additionally offer the opportunity for the translator to act as a subjective filter — or, instead of a translator, there could simply be fewer NPCs that can sign, so they translate for those who can’t, though the same filtering opportunity then exists.
The others who have replied here all mention that truly silent protagonists are often visually expressive, and I’ve seen this too! For a different example, Neopolitan from RWBY is mute, but the viewer never wonders what her thoughts and emotions are, since they’re always unmistakeably broadcasted through her expressions and actions. Her style is also matched by none, and in fact, she’s one of the most popular characters of the anime.
Here’s the shortest yet still mostly effective video I could find that explains it a bit more:
Another example of a silent character (though this depends greatly on the media in which he appears) is Pokémon’s Red. In the games, he barely ever speaks — his lines mostly consist of “…”, “…?”, and “…!”) — but this is because he has significant social issues. Most people wouldn’t disappear off the face of the world to go meditate in a mountain for several years without any regard for those they leave behind.
So, yeah, there are many ways you could depict a silent character. If you choose not to have them speak in any way, then “show vs tell” will be more applicable than ever.