It’s not possible to do it completely without the use of an extra add-on because the database entries need to be searched and replaced which can not be done manually for all entries. So wp migrate db is the best tool for doing this.
If there are no database changes, its simple:
– Copy all files located in the staging subfolder folder (excluding the wp-config.php!!!) back to the root folder of your main site.
– Overwrite existing files. (Do a full backup of the main files first!!!)
If there are additional DB changes:
Use additionally a tool like WP Migrate to copy back the database content.
Another option would be to make the staging site the live site with redirecting the server to the subfolder but this includes additional modifications as well.
I recommend to copy the files from the staging site to the live one so you keep the staging site for further testings.