Can I get my log book issued before the event?
Yes, absolutely you can. Bring the car to one of the scrutineers and they'll be able to log book it no trouble, assuming everything is in good shape of course.We prefer that you start this process early. Waiting until the day of the rally for a scrutineer to see your brand new rally car could add time to the tech inspection, and if you need to address anything, it leaves very little time to fix it.
The scrutineers aren't on-call though: they have their normal lives and jobs, and don't take vacation days to travel around to issue log books. So it will be you visiting them.