Is it possible to recover a Pages document I may have accidentally deleted?

Here's 2 ways to try to recover that file: 1) look for a "data recovery" company in your local area that knows how to handle Apple computers; or try the service offered at Drivesavers: https://drivesaversdatarecovery.com/. Or 2) do it yourself by following the guidance on Yourtube videos such as: https://www.youtube.com/watch?v=Cz_Z8KoBKQA

And do this very soon to avoid or minimize how current activity may over-write on the file.

If you quit Pages with unsaved work, it is lost forever, and quitting also causes Pages to clean up any temporary files associated with the work. This is expressly why you save a blank document before you start entering any Pages content so autosave is enabled and you don't lose work.

For autosaved Pages documents, you really should also have Apple's Time Machine backing up to an external drive every hour. That gives you a means to retrieve a document from a given backup timeframe.

Ignore the data recovery company suggestion as there is simply nothing to recover under the circumstances. Even if you had produced, saved, and then accidentally deleted a Pages document with the Finder by moving it to the Trash and emptying the Trash — you are on a UNIX machine and once something is deleted, it is marked for System reallocation for other storage requests.