Can I control a Mac Mini (with VNC) from a PC notebook the very first time I turn it on, just after purchase? I mean: it has no mouse, keyboard and screen but I guess it has to be initialized.
Can it be remotely controlled just after unboxing?
No, it can't. In order to set up the Mac after purchase, you have to go through some basic process, like watching an introductory movie, entering your user data, setting up a password, registering with Apple, et cetera. Only after that, a user account is created, which could then be configured to enable screen sharing (i.e. the VNC service).
The VNC service could theoretically be started via command line, even remotely, but that would mean you'd somehow need to get to the device before anyway, be it using a real keyboard/mouse or having remote access before.
So, no, there's no unboxing and instant remote access. Think about the security consequences. You couldn't even provide login details if you haven't set up a user.