I have the credentials to login to a server via ftp, and from here I want to create a SQL database. Can I do this, and if so how? Thank you.
No. Or, you are looking for something like SQLite wich is a database stored in a file.
FTP is a protocol that allow to write and read files to/from a server.
Running a SQL server means you need to have the right to execute applications. FTP may lt you write an executable, but you won't allowed to execute it. It's the case of MySQL, MariaDB, Postgresql, and many SGDB.
If you really need a SQL database and all you have is only a FTP access (And probably running php web pages, as it's often the case on web hosting services), take a look at SQLite. It's not a "true" database, but for a basic usage it can provide useful functionalities.