What is the easiest way to find out domain traffic?

Question

Web traffic analysis

They gave me a domain, until I hooked it to hosting, search engines say little by little that they knew such a domain, someone even refers. But for some reason it seems that decent traffic goes to it. I want to hook up to hosting, but I don’t know what to do next; Is it possible to attach Yandex Metrika, Google Analytics, etc. to an empty site? Or maybe even some kind of advertising?)
Is there any ready-made tool so that you can find out as much as possible what is happening with the domain (who comes in, where the traffic comes from, etc.)?
So far, only look at the logs in my head, but there is little information there.
Well, if there is traffic, what would you put on the site? something like a chat maybe?) let them chat among themselves, maybe they will say how they go there)