Pages document exported to word, minimized, can't find it

Pages probably would save that exported Word document in the last folder that you used to save any previous document — unless you explicitly changed the save destination folder. So, if you are using iCloud, or any other Cloud destination, it might be worth looking there.

Check in System Preferences : Spotlight : Search Results. At minimum, are Documents, Folders, and Others selected? if so, and you are unsure if you have been using Spotlight to index your startup drive, click on the Privacy tab in Spotlight, and then drag and drop your Macintosh HD drive icon onto the open Privacy panel. Wait 10 seconds, and then select it, and click [-] to remove it from the Privacy panel. This will start Spotlight indexing your startup drive. After about 15 minutes, do the following Spotlight search from the magnifying loop in the top right menu bar:

kind:word created:>01/01/2020
kind:pages created:>01/01/2020

You can press the ⌘ key to see the path to the document, and ⌘+R to open a Finder window with that file icon selected.

These two Spotlight searches will locate any saved .pages, or exported .doc/.docx documents that were created since the first of the year. If you were saving to the Pages folder on iCloud Drive, and subsequently unchecked that entry in System Preferences : iCloud : iCloud Drive : Options…, then that Pages folder would not be shown, or available for search.

It will either be minimized in your Pages Dock icon, or on the right-end of the Dock.

Minimizing the window does not close the app or affect the actual file in any way. You can always open it from wherever it is saved on your hard drive, by looking for it through Finder.

When minimized a preview of the document will be shown on the right most side of the dock. Look for the file there to open it again.

Or simply open the Word app again, and open it form the recent menu.