You typically do the financing couple days before you leave for your trip. They might of course run a credit check and all that jazz beforehand though. But the 45 day count down doesnt start till you completely fill out the paperwork right before you leave.
They wont let you pick up the car at the Welt unless its paid for.
My car made it to the U.S right when my first payment was due if that helps.
2009 E90 M3