He created a number of programs like the Works Progress Administration that employed people to work in parks, dig holes, fill holes, do stuff and get paid. This doesn’t, on the surface, look like it would prolong a depression. In fact, isn’t it nice that people who were begging for work could have something to do that paid a wage?
Of course, a little deeper common sense suggests that beyond such work, the wages that business could afford would be in competition the government program. This means your business would have to wait to be able to afford the labor. That is only a small part of the total picture. Other nations also faced problems in the 1930s due to the worldwide depression and some did better than others.
If a govt program puts constraints on business or is anti-business, that program would slow business founding and recovery. Also, higher taxes and legislation to favor labor organizations that pressure business will slow business recovery.
It is difficult to compare the US with another nation to get a sense of the effect of FDR’s policies on the depression because of a lot of differences between countries. However, you can compare the US in the 30s to the US in the 70s or even 1837 and see differences. One difference is the time to recovery.
On the other hand (isn't it great that economists have so many hands?) if businesses are already having to compete with the welfare office which pays people for doing nothing, isn't it better that people actually do some work for their government check?