You could add a CreateDate field formatted however you want.
Using Date Fields in Microsoft Word

This field is linked to the date (and time) that a document is initially created. Seconds can be included and it need not display as a typical date and time. Note that using SaveAs on such a document changes this date. You could, though, unlink the field after it is inserted to freeze it even if SaveAs is later used. (Ctrl+Shift+ F11) unlinks fields.

No macros are required.

Cross-posted at IT Pro Discussions