I didn't say his actions pulled us out of the the Great Depression, I said they saved the country. Now this is second hand but it comes from a source I trust implicitly. My father told me that this country was on the brink of anarchy during the Depression. He said there were agitators pushing us towards communism, there were agitators pushing us towards anarchy for anarchy's sake, and there were agitators pushing us towards fascism. Some of the action FDR undertook saved us from that. One that was very unconventional was his fireside chats. It calmed the nerves of a country in shock. Mow, my Dad was about as Republican as they come and he didn't particularly like FDR, but he could give credit where credit is due. Which, by the way, is something that is missing in today's polarized world.
What pulled us out of the Great Depression completely was WW II. We ramped up to just about full employment PDQ. Sure, we were already headed in that direction but WW II got our industry moving in a way it had never moved before. They called us the arsenal of Democracy because we produced a tremendous amount of material. It can be argued that we produced more than any two other of the major countries.