I was in a similar situation with a Siamese Mauser converted to 45-70. I initially did see a serial number you'd expect to see in the "usual" obviously visible places. Took it to a smith and he told me the same as PJ above. Then he pulled the barreled action from the stock and found the original serial number under the receiver. Because that was there, he could legally stamp the serial number in a visible location above the stock line and the caliber on the barrel.
Yes, to what others have said. US Customs will need to see the serial number to issue the 4457. Then when you go thru to the country you're entering, they will compare you 4457, to the import permit and the same when you leave said country. Then when you re-enter the US, US Customs will need to see the serial number again and compare against your 4457 too.
