In Subscriber Management, you can see a user's original subscription date.
Important Note:
If the subscriber signed up prior to 2012, their subscription date information may not be available.
Who can use this feature?
This feature is permission-based, a user will see the subscribers based on their rights of the modules that send notifications.
Instructions
Navigate to Modules and on the Site Tools tab, select Subscriber Management:

Find the subscriber or list:

Module: Select a module
Category: Select a category (or all categories) for that module
Search Term: Search by Email Address or Phone Number
Search: Click the search button to retrieve results
View their subscription date in the far-right Original Subscription Date column:

To sort by Original Subscription Date (either Ascending or Descending) click the Original Subscription Date column header:

Up Arrow: Sort from oldest to newest
Down Arrow: Sort from newest to oldest