By accompanying the binary with a formal description of the possible arguments, either as a separate file or embedded in the executable. But the latter is not really sustainable the more metadata you add, so more likely a separate file.

Applications already come with lots of metadata: man pages, icon, readable name, ... adding formal shell-completion information is just another one.

Besides that, the built-in command line tools already have auto-completion for their arguments. Though I think they do it by running scripts at shell startup, which isn't exactly the mechanism I would have used... but it works.

In your case, "that a.out I just compiled", this metadata would be missing, so no shell completion for you. But that is a niche use case anyway, and not at all what this post is about.