I created a new Gmail address for CloudKit testing purposes only, and invited this address to join my team on App Store Connect. I see the new account in the "Developer" part of the Users page.
But when I try to add this new user on the container permission on the CloudKit dashboard, I only see me (my main owner account) and not the developer email address I just created.
Can free developer account added to an Individual Apple Developer Program team access a CloudKit dashboard? I really need this to test my app and see records in the private database (log the new user on the Simulator and a device to test sync is working, etc.).


Yes, this can be done. Make sure that the new account has been fully set up as an Apple ID.
Usually this process isn't final until you sign it at appleid.apple.com with the new account and accept any terms and conditions.
Once that is done, try signing into the CloudKit Dashboard again and see if the name appears. If it doesn't, try re-inviting that email from the developer portal.