The Packard Accessory number PA-xxxxx usually found on a label somewhere on the side or back of the radio enclosure would be the best way for 51 and later radios because those are listed in the parts manual. Earlier than that and I find nothing listed in parts manuals but maybe someone has a copy of the dealer sales lists for accessory or options showing the PA numbers that were available for the radios fitting the different models.
Without a sales list, another possibility with having the PA number or if available, the manufacturer's model number, is a chance of finding an aftermarket schematic. Those are common and usually have a print date or copyright date somewhere on them. That date could only narrow it down to a year or two because some radios were available more than one model year or diagram could have had a revision.
Here are some examples. The photo labeled "47 schematic" shows the copyright date which is typically on an aftermarket Sam's Photofact diagram. Those are often found in sets on ebay and sets can cover several different items. Many times a diagram with a radio year or a when printed date will be found glued to the back inner cover of the radio case such as that shown on the photo labeled "inside of case".