Currently, only users with admin-level access in WordPress can set up and use the Site Kit plugin. This guide explains the permission levels for Google tools when used with Site Kit:
Google Search Console
If you’re an admin in WordPress, Site Kit grants you Owner permissions for your site in Search Console. Learn more about permission levels in Search Console.
Google Analytics
Learn more about permission levels in Analytics
Tag Manager
To set up Tag Manager, you need to have container-level permissions in Tag Manager. If you don’t have access, get an admin to add you to the container in Tag Manager. Learn more about permission levels in Tag Manager.