IS there a way to add hundreds of users to a Public Group

Hundreds of Employees share the same 1 Profile but several Roles across the Role Hierarchy. 

I need the Users in this Profile to be able to view and edit each other's Cases. 

OWD for case is set to 'Private' and cannot be changed. 

I am not allowed to create a New Role

Solution: 

Create a new Public Group 

Add all users in this 1 Profile to this Public Group

Create a Sharing Rule on the Case object which allows users from this Public Group to view and edit Cases owned by users who are members of this Public Group. 

Is there another solution? 

If not is there a way where I can add hundreds of users to a Public Group at the same time? 

Thanks! 

Minhaj