I have a Singer 212W140, and the serial number is stamped into the bed's casting right below the model number plate. Yours may be somewhere else, but it will be stamped into the casting somewhere. In this case, the serial number is PA924072. The only thing you need is the first two letters. PA to PY means this machine was built between 1954 and 1963. Because of the numbers, my guess would be this one was built in 1955 or 56.
No one lives forever, the trick is creating something that will.