ZIP codes are a system of postal codes used by the United States Postal Service (USPS) since 1963
Obama was born in 1961
Getting an SSN for a child was, and still is, voluntary. It only becomes necessary when the child enters the wonderful world of taxation. In my case, I was about 10 when my parents opened a bank savings account for me. It was then that I got my SSN, with the correct prefix for the state I lived in.
Since Obama was taken to Indonesia as a child, it’s likely that he didn’t have an SSN at that point. Any suggestion that he applied for an SSN while in Indonesia is ludicrous.
So, it’s entirely likely that he was still SSN-free when he returned to Hawaii, and needed that SSN to get his first job.