Determine the exact date of creation of an Apple ID Is it possible to determine the exact date and time (if possible) of creation of an Apple ID? 

Is there any official or unofficial way to establish this if you don't have the initial sign up information recorded?
You can request a copy of your data that Apple has (Apple ID account and Device Information) by visiting https://privacy.apple.com.  It can take up to 7 days to prepare the report and you will have up to 14 days once it's ready to download it before it's deleted.
You will need to login with your Apple ID, password and two-factor authentication token.  You will be able to select what data you wish to download.
Select Data to be downloaded...

You will then receive an email from Apple confirming the request...

When you Receive your report.
My report came in 4 days after the request. It was an email message that takes you to a secure Apple website (you must authenticate) and will allow you to download your report.
There were 3 files in mine.  The Apple ID &amp; Account Information.csv is the file of interest.

After opening it in your application of choice (Excel or Pages is probably best), you will find a &quot;Created Date&quot; for your Apple ID in chronological order.  So, looking at mine, my ID was created 5/13/2009 (not the actual date, I changed it for this answer).  It includes the time as well; select the cell to see the time stamp.

Why so many entries?  Everytime you update something, your address, your credit card info, your sharing, etc. it creates an entry.  So, you may see many entries for the same Apple ID.
This report will provide you with every bit of information with respect to your Apple ID account info from creation to the last update.  A lot of columns were hidden for privacy, but I encourage you to explore the report(s) to see what data is collected.