Requirements

• Active community members (free or paid)
• Access to Admin Settings > Members > Access Groups

Steps

Create an Automated Group with the Visibility set to Badge 

Set a Filter for "Joined On" and fill in the timeframe

In this case, we give a badge to any user that has joined more than 360 days ago. You can also add additional filters that exclude specific members. Use the "Preview" button to check if you are targeting the right group of users.

[Optional] Set up a Workflow with a custom email to thank any new members of this group.