If you have cPanel > PHPMyAdmin, you can import a database there into one that already exists. So, you can go to cPanel > MySQL databases area, create the database, create the database user, add the database user to the database, then go to cPanel > PHPMyAdmin and import the database there (usually, an .sql file is what you'd be importing).
If this is a new WordPress install, you don't need to import the database either. A new WordPress installation (not a pre-existing one being moved) would simply create the database during WordPress install.