When talking about these things there is a meta level we are targetting that you're not understanding. Types exist at a meta level and are part of the language.

Assembly language does not have types. What you can do is create a new language with assembly and have that language have types. The reason why it has to be done this way is because these types of checks CANNOT happen at runtime. It's a pre-runtime check that prevents the code from even running if it's not correct.

Think about it. Can you add types to assembly language without creating a new language? No.