When to give notice to current employer

Hello - I'm an American about to sign a contract for a job in Copenhagen.  My Danish employer is going to apply for a Fast Track work permit, and my plan is to be physically in Denmark within 14 days of the application being submitted so that I can do biometrics and get a "quick job start" provisional work permit on the same day.  My question, particularly for anyone else who did the Fast Track scheme with a quick start date (but of course I'll take relevant advice from all others), is whether I'm taking a risk by putting in my two weeks' notice with my current employer and then heading to Denmark without the work permit being officially approved.  Is there a chance that the fast track permit and/or the quick start will be denied or delayed, thus leaving me in Denmark without the ability to work for however long it takes to be approved?  Based on a thread in this category, the fast track approval process seems to be coming in at about a month and a half after biometrics, but again, I'd be seeking an immediate provisional work permit based on a quick start, not the regular fast track process.  It seems like the quick start process is basically a rubber stamp as long as you meet all the requirements, so I feel pretty confident I can get it done, but want to know what the potential downside(s) could be.  Thanks!