Without root access you have no way to configure your server to use a HTTPS at all.
There may be hosting providers supporting it...
...or - if your hoster provides another way to add the TLS certificates - you may be able to use the webroot authentication method: Using the webroot domain verification method - #8 by chrisc
But before I'm talking rubbish - as I'm not really sure whether the webroot method would work in this case - I've created a new topic to discuss this independently from a Raspberry Pi:
Edit: Webroot method is not suitable for shared-hosting.