My parents arranged SS#s for myself and my two sisters shortly after we were born, and that was in the fifties(19).
Right. You COULD get SS#s early, but you did not NEED to have one until you had a job or otherwise needed to have taxes withheld from income, so most people back then didn't get one until their first "paycheck" job.
Was the reason why they got you SS#s that they put taxable-income-generating assets in your name?
Very unusual. Because I and my friends did not apply for an SS number until we started working our first jobs (for me, a part-time one in 1965).