This is one of the cases where there's sometimes confusion between the semantics of Julia as a language and the practical implementation of Julia -- just like how Julia is dynamically typed as a matter of language semantics, but compiles to a statically-typed intermediate representation as an implementation detail [1].

While it is not part of the language semantics, there certainly is, in the current implementation, a time at which any given method in Julia is (JAOT) compiled (via SSA-form IR, LLVM IR, and finally to native machine code) -- and whether or not types are able to be inferred at this time is sufficiently important that it has its own name: type stability [e.g., 2], with type-stable code being generally a couple orders of magnitude faster than equivalent type-unstable code.

[1] https://stackoverflow.com/questions/28078089/is-julia-dynami...

[2] https://www.juliabloggers.com/writing-type-stable-julia-code...