Mr. Burns’ Social Security Number is 000-00-0002. Although this is a joke on Mr. Burns’ age, in actuality, the first three numbers of the SSN represent the state in which the person was born in. There is no 000 prefix.
In one episode, the family visited the Five Corners. This does not exist, but there is a Four Corners.
So if Springfield does exist outside of the TV show, it’s in a state that borders Utah, Colorado, Arizona, and New Mexico which uses the Social Security prefix 000.