So just to clarify, you’ve already setup the multisite by following:
https://codex.wordpress.org/Create_A_Network
And the multisite is working and you can create subdomains. But you want your current site to be a subdomain?
If so, I think the best way to do this will be to create the new sub site first, then use a cloning/migration plugin to copy all your data from your current site to the new sub site. WordPress has it’s own export-import plugin:
https://en-gb.wordpress.org/plugins/wordpress-importer/
The WordPress Importer will import the following content from a WordPress export file:
- Posts, pages and other custom post types
- Comments
- Custom fields and post meta (this will include your post thumbnails and attachments).
- Categories, tags and terms from custom taxonomies
- Authors
Then you can remove all the data on your root site.
There are other cloning/migration plugins if you don’t like the WordPress importer.