Option: install WordPress in parent folder domain.com. Copy installed themes, childtheme, plugins and so on from subfolder ‘beta’ to parent folder. Add wanted users.
Then export beta-site and import this into ‘new-site’. Categories, menu’s and media will be moved while importing. You can connect posts from beta-users with users you added to your new-site.
You have to adapt the widgets again and tell the theme wich menu should be shown as primary.
Perhaps, when you install WordPress in the parent folder, you can connect it with the same database you used in the beta folder. I have no experience with that.
Or you can keep the installed beta-database separated and use this beta installation for further development.