How to make the user belong to a specific group once he creates the account
You can add users registered with specific email domain to automatically added to a group.
Go to Group >> Manage >> Membership and in Automatic section add specific email domain.
You can do that with an invite How to send, configure, and accept invites to a Discourse site
An alternative is to use the Custom Wizard Plugin 🧙 to have a wizard handle it.
This is particularly useful when you need to sort folk into several groups based on their answers to the profile / joining questions (or additional questions in the wizard)