Is there a way to view who created a permissions group and when it was created - from the Site Admin level?
SharePoint by default doesn’t display this information in the user interface. To check the data, you can enable audit settings for site settings and automatically save the report into a library. Note: to enable audit settings, you need to have site collection administrator's permissions.
Then if a user creates a group after that, the change will be logged into audit log. Site administrator could check the report to find the creator of a group.