Here are some ways to determine when your radio was built:
1) Date sticker in the battery box
2) Date molded into the plastic case (this is usually inside, so it requires disassembly to find)
3) Date sticker on the tape motor (but this only tells you when the motor was built)
4) Date marked on the circuit boards
5) Date code on the microchips (after the 5-8 digit main code)
6) Date printed on the service manual (you can find images of it on Google)
7) Date of any advertisements or catalogs you can find on Google
I prefer the last two methods, because I want to know when the radio was first introduced, not when it was manufactured. Many radios were manufactured across multiple years. So even if there's a date stamp saying your radio was built in 1988, it could have been introduced 2 or 3 years earlier.