Which system catalog view has the create_date of a database which name was modified?
Which system catalog view has the create_date of a database which name was modified? Or an alternative reliable method if such view doesn't exist.


You're correct in your assessment of create_date in sys.databases, which is confirmed by the documentation:


  Date the database was created or renamed.


So the create_date is the ideal value to use as the end time of the refresh process, being that the rename is the final step. 

That being said, given the restrictions in place here I don't think you'll find any more accurate of a start time than the timestamp on the first table. 

So the unsatisfying answer is you're as close as you're going to get, I think.