Several weeks; it really depends on whether they ask for more documents/proof so that could hold the process up.

Here's the link for what any employer has to do to hire a non-EU citizen:

https://www.bfm.admin.ch/content/bfm...zulassung.html

This is time consuming and expensive so employers aren't going to do it unless they have a good chance of a successful permit application.

At the moment any EU national who doesn't have a permit allowing them to work here is facing a similar process due to a quota limit being put on 5-year B permits. So any employer has to prove they can't find a Swiss national or someone else already living here who has a "work" permit who could do the job.