How do I delete a folder that I did not create in SharePoint?

Hello kaseyearhart

you need enough rights to delete a folder: https://support.microsoft.com/en-us/office/customize-permissions-for-a-sharepoint-list-or-library-02d770f3-59eb-4910-a608-5f84cc297782

You must have at least contribute rights, or higher. 

Unless it has its own folder permissions, then you need higher permissions.

Best, Dave