I did speak in haste earlier. The unemployment rate at the beginning of WWII was 17.2%, extraordinarily high by any historical standard.

That WWII pulled the US out of the Depression is considered common knowledge by most economists. Here are some reasonablly independent sources that support that contention with a relevant quote taken from each.

The Great Depression -- Wikipedia
"After the Court began to uphold his interventionist legislation, the economy took a sharp downward dip, which has been called a depression within a depression, from which it was only slowly recovering when the US entered WWII. Thus it is claimed that his intervention delayed the economic recovery that had been underway."

The Depression & WWII -- Library of Congress
"The end to the Great Depression came about in 1941 with America's entry into World War II."

The Timeline of The Great Depression -- PBS
"...In little over a year, following Japan's December 1941 bombing of Pearl Harbor, the U.S. would enter the war in the Pacific and in Europe.

The war effort jump-started U.S. industry and effectively ended the Great Depression."

The Great Depression -- FDR Presidential Library and Museum
Despite all the President's efforts and the courage of the American people, the Depression hung on until 1941, when America's involvement in the Second World War resulted in the drafting of young men into military service, and the creation of millions of jobs in defense and war industries.