Hi Don,
A teacher needs a Teams-enabled Microsoft 365 Education license (A1/A3/A5 for faculty) and permission to create Microsoft 365 Groups in your tenant.
Creating any team (including a Class team) creates a Microsoft 365 group under the hood, so if group creation is restricted, those teachers must be added to the security group you've designated as "allowed to create Microsoft 365 Groups". If you leave group creation at the default (open), any licensed teacher can create a Class team without extra privileges.
To do this, confirm the teacher's account has an Education faculty license with the Teams service turned on in the Microsoft 365 admin center, then make sure they're either not blocked by a group-creation restriction or that they're a member of the "allowed creators" security group you configured in Entra ID. Once that’s in place, the teacher can go to Teams > Join or create a team > Create team > Class and set up the class.
Note: If your district uses School Data Sync, you may already be auto-provisioning Class Teams with teachers set as owners, in which case they don't need to create classes manually.
I hope this helps!