You don’t really provide enough information to give a full answer (There are many different shared hosting plans at godaddy).
You need to prove ownership by either adding “tokens” to your site, that can be reached by http, or in your DNS records.
You say you can’t install using SSH, but do you have SSH access to the account ? if so you can use many of the alternate clients, run on your account to prove ownership, then paste the cert using your browser.
If you don’t have SSH access at all, then you may be better using the DNS challenge to obtain a cert, as that can be run from anywhere. Alternatively use one of the browser clients.