Create WordPress website without separate hosting?

I’m the new web admin for a nonprofit organization and our website account appears to have been deleted by someone when I was out of town recently.

I am trying to recreate the site and was told that we didn’t have a separate website hosting company, which sounds odd to me esp because the domain name is stand-alone (it doesn’t contain “wordpress” in it).

I’m new to this aspect of websites so can anyone please advise whether it’s even possible to have a WordPress website without separate hosting?

Thanks!
Ginger