A mailing list could be configured to allow new emails only from list managers, which sounds like what you want.
Any other solution is going to require you to do something manually to enable and disable the group.
If you have a script that creates the group and adds existing users, you could simply delete the group when its not in use and run the script to create it when it's needed.
In case you're a fan of
rube goldberg:
- Create a gmail address, then configure 'rules' on that mailbox to forward anything from approved managers to your staff. New Users must be added to the rule, and departed users must be deleted.
- Do something similar on the SME itself: create an actual user (instead of a group), then use mail rules to forward email from managers to active staff
- Teach your managers how to create groups in their address book, and have them manage who gets the emails. Use "to:" the HR person and "bcc: the group from the address book
- Keep the active user list in a google sheet, and create a hyperlink in that sheet to start an email that bcc's all of the active users. Share the sheet with managers. (this requires google sheets instead of excel due to the 254 character limit on formula length in excel...). Here is an example google sheet showing what I mean:
Google Sheet Mailing List Example