Settings > Administration > System Settings (or settings > Email configuration > Email configuration settings)
Look for the two checkboxes “Process emails only for approved users / queues” and uncheck (clear) them.
Now you don’t need to approve users before they can use email.
If the person who sets up users is the same person who can approve the mailbox for use, then it makes sense to turn this off. It only really adds value when users can be created by one person (maybe in the systems team) and the mailbox needs to be approved by someone on the CRM team.