Enable Partial Search matches for document lookup?

Our restaurant POS stations don't have a barcode scanner, so when we need to search for previous order records, the full-length document number (including the document class number and leading zeroes) need to be typed into the search box in order for us to locate the record.

Would it be possible to update the search algorithm to include *partial* matches along with exact matches? When our order sales records are still only in the 3-4 digit range, having to type in 12+ characters to lookup a receipt every time is a bit time-consuming.