Is it possible to hide Public Pages for non-site members while building the site?

Issue

Is there a way to prevent indexed Google pages from being searched by non-site members while building a public internet website using Liferay DXP?

You can restrict public access to your site by changing its view permission for site admin/admin role users.
For details, kindly check the following article: https://help.liferay.com/hc/en-us/articles/360018156131-Roles-and-Permissions
You can also revoke Guest's view permissions from all the pages comprising the site.
For that, you go to the page tree, select the page, go to the 3 dots icon, and click 'permissions'. Find the Guest role and remove 'view' permission.
- This may be the safest way.
Something like this might be doable too:
Remove the public page set's virtualhost while having a private page on a different virtualhost for login.
It's a general practice to configure a virtualhost for the production instance. It's best to turn on this functionality in Liferay too, under the configuration of public pages. The idea is to disable this connection, so that guest visitors will get a 404 when reaching the site. While using the virtualhost of another site may be used to reach the login page.