For all you youngsters- at one time, members of the Armed Forces had a "Service Number". That stopped July 1, 1969. Those that entered service after that date never had
a Service Number.
Supplying your SSAN is voluntary- it may speed up the process if you have a common name. I have one friend that is the only person in the US (so far as we know) that has that first and last name. But if you are Robert Jones, odds are that somewhere, a Bob Jones has been in trouble. (have another friend that is a retired Police Captain from Virginia- John Smith. Yep- Cpt. John Smith of Virginia. Don't ask him about Pocahontas)
Me, I had TWO service numbers. One when I was enlisted, one as an officer. Wonder which one they would want for me?