SSL with WP admin, but without hosting access

One of my clients asked me to remake their old site which is still in HTTP, and I need to install a SSL certificate to make it HTTPS.
The problem is: they are unable to provide the login details of their hosting plan.
Apparently the old webmaster disappeared, they don't know the hosting or FTP credentials, and they only have access to WP admin.
Is there a way to install a SSL certificate through WP admin only?
I've seen some plugins like Really Simple SSL, but they all seem to require hosting access to actually install the certificate.
Cloudflare isn't an option because without hosting access there's no way to change the nameservers to use it.

Installing a SSL certificate is something you do with the hosting company. You can't do that in Wordpress alone. An alternative solution is you could use CloudFlare. However, you'll need access to their domain name. And if their domain name is with the host then you're SOL. Often times clients will register with a different company than their host so this could be a possible solution.

Just move them to another host. Seems like the best thing to do, if they can not access their hosting account in anyway.

I think it would be better to install a backup extension, and move everything to another hosting where your client has access to cPanel.