Is there a way to recover deleted Pages files on my Mac?

For clarity, macOS is a UNIX operating system and when one deletes a file, it is marked as reclaimable storage by the operating system. Any new file addition to the operating system is a storage allocation request and the operating system will repurpose the reclaimable storage for use in meeting the new file storage requirement. Once that occurs, there is no recovery possible with any software intended for that purpose.

There is no fixed timeframe by which the first paragraph occurs. It might be five minutes, or a day, depending on how active the Mac filesystem requirements are for new storage. Certainly, for the OP to bring up this issue a full two years later means the deleted files are no longer recoverable by any means — unless storage allocation was frozen by shutting down the Mac and not reusing it immediately after the files were deleted.

Pages documents are especially problematic as they are assembled in a manner by Pages that is known only by Apple, and the contents of the documents are internally encrypted to avoid users or tools from decyphering them.

When you delete Pages documents and empty the Trash, the files are gone forever. The operating system sees that the files are marked as such and will reclaim the contents for new storage allocation. Not having Time machine running ends the story as there is no possible recovery of the deleted files. Two years later, there is nothing that you nor any Apple Store, nor Apple Service Center can do to recover the files.

Apple's iCloud has a 30-day sliding window to restore files deleted on it and beyond that timeframe, there will be no recovery possible.

You've tried everything you can do to restore the files, you didn't have any backup, and the files were deleted 2 years ago, even you have downloaded software, it seems a mission impossible. Which software did you download and try? Disk Drill?