I'm sorry, but you are incorrect. Life expentancy AT BIRTH was arround 66 years in 1937. But that number is very deceptive, because of higher infant mortality. The life expectancy of someone reaching 60 was about 11 years. So it was known all along that people would collect. And in the beginning, there was one lump sum payment when you retired - monthly benefits came a few years later.
But the increase in life-expectancy is certainly a factor in the insolvency of Social Security. The only way to get around the problem is to limit benefits and allow most of a worker's contribution to go into a private account.
The advantage of a private account is not only that politicians (theoretically) can't spend it, but it can be invested more efficiently. An investment in the stock market, over time, yields about a 5% real return (return above inflation); the government bonds SSA is forced to invest in historically have a real return of 2%. Over 40 years it makes a BIG difference.
Monthly benefits started 3 years later...1940. The first recipient lived to 100 and collected almost $23,000.