Looking to find a way to sort cursor without adding either an index or a new field in the document

So I want to sort a collection at publication using a function. If possible, I’d rather not have to create a new field in the document with which to sort by, and instead be able to do a comparison real-time (so that a user can potentially change the sorted results, with pagination). Is it possible to sort a cursor/collection at publication without needing a field with which to sort by, and instead sort by a function?