The Great Depression was a period of economic distress that did not directly help the United States become a global superpower, but it set off a chain reaction of circumstances that indirectly led to that outcome.
First, the Depression was a global crisis that spread to Europe. It undermined an already highly unstable situation in Germany, helping the National Socialists (the Nazi party) to gain an unprecedented numbers of Reichstag seats in the 1930 elections. This paved the way for Hitler to become Germany's chancellor—and soon afterwards dictator—in 1933.
With Hitler in power, World War II became inevitable, because Hitler was bent on war. Meanwhile, the Great Depression swept Franklin Roosevelt into power in the United States. Roosevelt was determinedly anti-Nazi and intended to intervene at the first possible politically expedient opportunity to fight the spread of Nazism. Although he soft-pedaled his pro-war stance during the 1940 presidential campaign, his re-election all but guaranteed that the US would abandon its isolationism and fight in the war on the side of the Allies—which it did.
The war catapulted the US out of the Great Depression as the manufacture of planes, tanks, battleships, bullets, and other materials of war, as well as rapid and massive mobilization, brought unemployment to new lows. The U.S. factory system geared up to the highest possible capacity to supply the war effort, with production usually running around the clock.
After the war, the devastation in Europe and Asia left the US as the only country with a completely intact and robust industrial capacity. The economy surged, and since the US was the leader in a victorious war effort, it became natural for it to finally assume the superpower mantle it had shied away from in the past.