This actually is possible. Basically, you need to add a secondary domain (not an alias) and then execute this Google Directory API request:
PUT
https://www.googleapis.com/admin/directory/v1/customers/my_customer?fields=customerDomain&key={YOUR_API_KEY}
{"customerDomain": "my_new_domain.com"}`.
You can run this command quite easily, at the time of this writing, by visiting https://developers.google.com/admin-sdk/directory/v1/reference/customers/update, scrolling down to the "Try It" section, and setting customerKey
to my_customer
, fields
to customerDomain
, and adding the field customerDomain
to the request body, with the value of your secondary domain that you'd like to make your primary domain (no www). Isn't that nice?
More detailed instructions are at http://www.saysjen.com/swapping-your-google-apps-primary-domain-to-your-secondary-domain-for-dummies/.