the proper fix is to pull the glass, remove all the old urethane adhesive, fix the rust that's likely there, and reseal it.
you're going to need to pull the carpet to even attempt to dry it out, so I'd advise doing that first, then do the window, then check for other leaks and fix any rust you find, then put the interior back. it's a royal pain, but it's the proper way to know it's done proper.