Hello,
Thank you for contacting Rank Math and bringing your concern to our attention.
I would suggest installing the Rank Math plugin on their site in the beginning (staging site) so that while they’re writing their content, Rank Math can analyze it and help them in real-time.
There is no unique way of treating a staging site/under construction that is different than the production/live site.
Once you have pushed your site to live, all the Rank Math settings you have made or imported from your staging site would still be intact.
The basic difference would be the indexing option, which you can easily set using the WordPress option to discourage search engines from indexing your site in WordPress Dashboard > Settings > Reading.

Other than this, you should treat the settings on your staging site the same as you would on your live sites.
You won’t however need to enable some modules such as Sitemap, 404 Monitor & Analytics on the staging area since they won’t be useful.
Hope that helps.
Thank you.
Hello,
Since we did not hear back from you for 15 days, we are assuming that you found the solution. We are closing this support ticket.
If you still need assistance or any other help, please feel free to open a new support ticket, and we will be more than happy to assist.
Thank you.