SS#was not obtained legally unless he was living in Conn. at the time, perhaps staying with or visiting relatives. Maybe his mother’s co-wife’s family?
Someone should get the SS-5 form for the number that was issued before his. That person is deceased ( Thomas Wood ), so it is available to anyone who requests it. That would show what day it was issued and approximately when it was applied for. If it was during the summer, then possibly he could have been staying with someone. But, if it was in the middle of the school year when he was in school in Hawaii - that is another story.