I would not normally be the one to defend FDR’s economic policies, but the recession began in October 1929, and FDR was sworn in March, 1933, so it was already 3-1/2 years old when FDR became President. Not only that, but the Depression bottomed the month that FDR was sworn in. I think that a better argument can be made that FDR prolonged the Depression. Most economists will tell you that the Fed was too tight on the money in 1928 and 9, and that is what triggered the downturn. It was Hoover’s interventionist policies, raising taxes and tarriffs, together with continued tight money that turned it into a Depression.
You are right. Hoover made it worse with bad tax policy and protectionism - Smoot-Hawley.
Friedman believed the Fed acted against the Bank of the United States, a Jewish owned bank, for anti-Semitic reasons, thus precipitating the banking crisis. They should have acted as the lender of last resort and worked out a minor situation. Instead they got a panic.
Check the rest of the history.