what to do for one who starts a faculty job before semester starts
At least for the US, the university generally has a specific date on which they expect new faculty to begin their employment - typically sometime in August for schools that are on semesters.  It's usually at least a week or two before the start of classes, to give time for various kinds of orientation / training / onboarding.  This start date is usually mentioned in the job posting, or during the interview process.

In principle you could negotiate an earlier date, but there'd probably have to be a good reason - something specific that you would be doing for the university during that time, beyond your usual research or course preparation.  The university has set their budget assuming that you will be paid starting on the designated start date, and is unlikely to be willing to start paying you sooner unless they are really getting something in exchange.  Indeed, most full-time faculty in the US are on 9-month contracts and don't receive salary during the summer months unless they are performing special services or have grant funding.

If you'll be arriving in the city earlier than your start date, it's reasonable to ask if you can start using your office, get a library card, etc, before your employment officially begins.  Your department will probably be happy to do little things like this as a courtesy to you.  And, of course, you can start meeting your colleagues and learning about the job.  You just won't be getting paid yet.