There's a few different ways to access a user's membership information and start date.
From Users List View
A User's Membership start date is visible directly on the users list view.
To view more details about a User's Memberships, click the "1 Membership" link in the Activity Column
You can then view information about each membership including the start date.
From User Profile
You can also view Membership details on the Memberships card on the User details screen.
By Hovering
You can access a User's primary membership by hovering the user and clicking their membership.