..and FDR led us out of it, by first spending on government spending on infrastructure with the new deal. Then putting the infrastructure to work when demand picked up during WWII. We are still in the building infrastructure stage of the recovery. Congress is impeding progress.
The Hoover Dam was a good project. The proper way to try to stimulate the economy. It provides jobs immediately and a return on the investment by the sale of power far into the future.
My guess would be a large part of what brought the US out of depression was the war, especially before the US got physically involved, through exports to the allies. Auto factories were converted to jeep, tank, etc production facilities. War ships were built on expedited schedules with minimal government bureaucracy to get in the way. (Something that would probably be impossible today. So we have to maintain a strong military always at the ready.)... More due to that the free market, patriotism and capitalism free of political correctness, special interests and America haters, than anything FDR did specifically.