Migrate Site

I recently had a client ask that I move their site from a previous web developer to us. Their previous web developer sent over their WordPress login and domain login, but no hosting login. The only issue with this is that I’m encountering a 504 Gateway Issue every time I go to the “Install a Plugin” page. I also have no access to their Cpanel or FTP.

I reached out to the previous web developer to fix the issue and they haven’t responded. How do I go about moving this site to our hosting without having to completely remake it from the ground up?

Any help is appreciated. Thank you