There are generally two reasons for the inventory to show a warranty start date.

First is if the car is a demo or staff driven. Warranty starts when the car is put in service. Those cars still show up on the inventory list. They usually aren't pretending that the cars are still new.

Second is if there are warranty claims soon after the car is received at the dealer, before it is sold. With another manufacturer I worked with (and I am assuming it can be the same with a new BMW) if a car came in and had a problem, the dealer had to start the warranty so that they could do the required repair and submit a claim to the manufacturer. The repair could be a campaign or update, for example. If the warranty wasn't started, they couldn't submit a claim. Then, when the vehicle is subsequently sold, the warranty start date was adjusted to the customer delivery date. Given that you were looking at an internal list, it is entirely reasonable that BMW has the same system.

Your warranty would be from the in-service date when you take possession.

edit: Saw the post from BCA, above, about BMW paying the dealer. That could work for any predelivery inspection or campaign work. With the other manufacturers I worked with, the manufacturer only paid up any sales rebates when the customer registration was done, and that required a customer name and address. You could put it in service for (interim) warranty purposes, but that didn't count as delivery without a name and address.

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2007 X3 3.0si, 6 MT, Premium, White

Retired:
2008 535i, 6 MT, M Sport, Premium, Space Grey
2003 X5 3.0 Steptronic, Premium, Titanium Silver
2002 325xi 5 MT, Steel Grey
2004 Z4 3.0 Premium, Sport, SMG, Maldives Blue