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.
For those who don't know JAOT stands for Just-Ahead-Off-Time and refers to the fact that Julias current implementation doesn't do many things associated with JITs today but simply calls an AOT compiler under the assumption that any function gets called often enough in this session for compilation to be amortized.
There are some weak mechanisms to prevent useless overspecialization such as @nospecialize and there are attempts to add smarter recompilation strategies by some packages.
Julia semantically doesn't have compile time type, but is free to (and almost always does) figure out the compile time type and use that information aggressively as long as doing so doesn't change behavior.
By "compile time", I meant the first time you call the function with a given type signature.
Also, that comment is saying "compile time type" does not exist. I don't know C++, so I cannot comment on it, but from the sound of Yu Yichao's comment, C++ has separate concepts for runtime vs compile time types. Julia does not (as already said by adgjlsfhk1).
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...