The Stock Market Crash of 1929 gave progressives an opportunity the opportunity they had been waiting for. They would use this as an opportunity to blame capitalism for the stock market crash (even though it was a progressive republican and not capitalism per se as you can read here), and make an attempt to further the progressive goals of creating a perfect society.
While classical liberal capitalist republicans ran Washington during the Roaring 20s, leading progressive advocates got together and decided they weren't going to be able to win over voters by a revolution. So they decided baby steps were better. Step by step, day by day, one program by one program, they would advance their agenda. That was the new goal.
Progressive was now a dirty word in the eyes of Americans, and therefore when Franklin Deleno Roosevelt decided to run for the office of the president, he was advised to run not as a progressive democrat, but as a liberal. Although he actually ran as a classical liberal (now known as conservatives), and then governed as a liberal (or really a progressive).
Hoover was a progressive, as is noted by his hike of tariffs ultimately helped lead to the stock market crash of 1929, and then he tried to help the poor economy by raising taxes and increasing regulations. This ultimately had the reverse effect he anticipated, and the economy did not improve. In fact, the result was a depression.
At this time it was not called the Great Depression. It would only get that name later. Yet that's beside the point. The fact that the economy got bad, and was not getting better with a republican president, set the table for the even more proggressive democrats to win over Washington in 1932.
Even though he ran as a Conservative, FDR's New Deal gave progressivism the credibility it needed. He continued to blame capitalism for what ailed America, and continued to advance progressive policies and programs.
Hoover was not as progressive as FDR was. FDR, however, and his progressive buddies, saw this as a great opportunity. They hiked taxes, hiked regulations, created so many government programs and agencies of people to tell us how to live and run our lives that I don't even think a great historian can name them all.
FDR ultimately used his new programs to give people the "candy" people needed to continue voting democrats into office for the next several years, while they continued to advance their agenda. Many people didn't like what he was doing, yet they still kept voting for him because he was at least doing something.
He told us his policies would end the Depression. They -- the New Deal -- Never ended anything. Unemployment increased. It went down occasionally due to short term government programs -- and usually right before elections. He used his new programs to buy voters to get re-elected, and told a desperate people if we create more programs we will ultimately get out of the Great Depression.
So FDR won, and won, and won and won.... The goal of creating a NWO was at full steam.