No, that isn’t normal at all.
Fluke or not, you should make use of all that traffic as soon as possible. You said that you have a clear vision of what you want the site to be? If I were you, I would put it into practice immediately.
Finish the site, fill it with content, and get it working. It may cost you a bit, but the potential will probably make the investment worth it. Perhaps you’ve stumbled upon a gold mine. Worst case scenario, the traffic will slowly taper down, but the visitors that do find your site useful will likely keep using it. Win-win.