All you can do is check the motor number. If it is the same E3667 that is on the paperwork you can be fairly sure the engine is original -- or at least has been in the car as long as the paperwork has been around. The first photo shows approximately where to look. It can be faint and covered with grease so you may have to clean and search.
As to the official vehicle number which is on the missing patent plate, if it is not also on the registration paperwork then there is no way to find it unless the build slip is miraculously still present. Those build slips were usually found taped to the top of the glovebox or at the fuel tank fill pipe but Packard didn't seem to have a fixed spot and they have been found tucked in all sorts of out of the way places.
If there is no luck with those suggestions, you can get close to the original vehicle number by looking at the "Briggs" tag or what Packard called the second body number which is somewhere on the firewall. The illustration shows it at "D" on the right side but location kind of varied by year. It is a small maybe 1x3" embossed tag which was placed there by the body builder. Because the order of bodies on the assembly line did not necessarily match the way they were delivered from the body builder the official number can be off by several numbers from what is on the tag. The only part which would be the same is the first 4 digits which denotes the body style. The last 4 or 5 numbers denote the sequence in production for that particular model and can be several removed from the tag number.
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