Is it possible to create a Team and add members, then have a user group created to reflect that Team

[WTS Support Team]

I am looking at possible solutions for a customer of ours. Currently, they are manually creating Teams, adding Team members, and configuring alerts in operations for email notifications.

After this, they go over to Atlassian Admin and create a Group with the same name as the Team, and manually assign the same Team members to that Group.

They are looking to see if it's possible to create or modify a Team and have those changes reflect in Groups.

The changes they want to see in Groups are...

- The Group name should be the same as the Team name.

- The Group members should also be the same members in the Team.

I've tried building out an automation but there are too many logical conditions for an automation to handle such as...

- Was a new Team just created?

     - If yes, has a Group already been created for this Team?

          - If yes, check if all members of Team exist in Group.

               - If yes, do nothing.

               - If no, add missing Team member to Group

          - If no, create Group and assign Team members to Group.

     - If no, was a member added to an existing Team?

          - If yes, does the Group already exist?

               - If yes, add new Team member to Group

               - If no, create Group and add Team members to Groups.

          - If no, do nothing.

* There is more logic to include but above gives a rough idea of the conditional logic needed, and then some. There are also variable scoping issues in and out of branches that are no fun to deal with and seem unreliable at this point.

Again, the customer wants to be able to manage Teams and Team Members from the 'Team' tab and have those changes automatically reflected somehow in Atlassian Admin --> Directory --> Groups. 

Does anyone have any suggestions or recommendations?