I would like to know if it is possible to set rest API endpoints from within a theme?

I created a class to do this and made an instance of the class in the theme's functions.php file. This triggers the constructor which calls the add_action() function. When I check the path, I get a 404 message saying this endpoint is not there.

Is there a way to make sure the endpoint created as part of my theme works? I assume that the theme is not normally loaded when the REST API is called.