I just did a Get Info on my user home folder (the home folder in Users on the hard drive). The creation date for that folder is shown as March 19 2011, which is dead on - that's when I first booted the Mac and created the account.
That folder was initially created in OS X 10.6.3, which was updated to OS X 10.6.8, then cloned, then updated to 10.7, cloned again, updated to 10.7.1, cloned again, and finally updated to 10.7.2. Yet the folder has retained its original creation date (which is to be expected).
Unless you have wiped accounts along the way, or done a total re-install of the OS at some time, the creation date for that user folder should get you very close. Factoring in the shipping time should get you to the actual purchase date.
In my case I still have the original shipping box; the FedEx label shows a shipping date of Mar 15 2011, which agrees with my recollection of shipping transit time.