Mysql connect without username/password

I build a new website for a client (WordPress is underlying) and have access trough FTP to his webspace. He does not provide or even know more informations than this because he had taken it from an former employee.

Is it possible to get know if any MySQL database exist on localhost and connect to it without the knowledge of an username or password?

I dont think that the web space host could help me with this problem, because they switched there business orientation a while ago and don't provide any new web space at all.