The Regulation and staff commentary are somewhat vague in that they say to used the "date received" or the "date on the application".
The date received is the date the bank actually received the application. Most banks date stamp when the application is received, absent a date stamp you would use the date on the "original" application.
the compliance officer for the bank i work for is using the typed application dated the same as the loan closing.
As an examiner your CO would have to prove to me that you received, processed and closed the loan in one day, otherwise I would cite you for LAR entry errors for the date application received field.