Hi @Nick Goltz,
Thank you for posting in this community.
We can create a security group in AAD, then put users who can create Teams groups into that security group, and then set it so that no other users except the group can create Teams groups.
For the exact steps, please refer to this article: Manage who can create Microsoft 365 Groups.
For creating SharePoint groups, you can create SharePoint groups as long as you are the site owner or have full control permissions.
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