Most shared hosting accounts don't have SSH. I had a shared hosting account at one time that allowed it but you had to fax them a drivers license. These accounts are typically used by people that may not even know what FTP is let alone SSH hence the reason they don't allow it.
The database can be uploaded a variety of ways such as using phpmyadmin, or in the case of really large databases you can FTP it to a directory and use bigdump
“Results! Why, man, I have gotten a lot of results! I have found several thousand things that won’t work.”
Attributed - Thomas Edison