Hey, let's discuss Military Keynesianism, government welfare programs, the effects of a nation at full employment and the creation of the huge US middle class!
The war helped bring the US out of the great depression, although it would be uncharitable to say it was the sole reason for the end of the Great Depression. The various programs under the New Deal had done much to mitigate the effects of the great depression (a topic for another post because my god the New Deal was huge).
However, when the US entered the War, government spending rose dramatically. The system of "cost plus"-contracts (basically the government buys something and promises to cover the cost of production plus pay a fair profit) under military Keynesianism meant that factories could hire workers almost indiscriminately, regardless of skill, and put them to work because the government covered the cost. The result of this was that everyone could find a job. Everyone. Women stopped being housewives and took jobs in factories, students went straight into factories from highschool, unskilled labourers could find jobs, decent paying jobs, on production lines. The US quickly reached full employment. It was not the most cost efficient form of production but in terms of quickly reaching staggering production levels, it worked.
A result of the US reaching full employment was that wages rose dramatically, spearheaded by the wartime industries (which would account for around 35% of GDP by 1945). With rising wages and almost unlimited opportunities for overtime the wage gap between white and blue collar workers narrowed rapidly. Along with several welfare projects and price control on a lot of food stuffs and other items the standard of living for the poorest in the US rose dramatically. The wartime industries attracted labourers from far and wide and government programs subsidiesed housing, daycare, pensions for the disabled etc, all in the name of increasing production. Access to better food through price controls and housing through various programs contributed further to increase the US standard of living.
By now you should be thinking, by god, that sounds brilliant but surely someone had to pay for all of this? And you're right. The US incurred a lot of debt during WW2, the national debt in 1945 was 120% of the GDP. So what happened when the US stopped massive military spending? Surely the system must now collapse? And it could have. But it didn't.
In 1945 the world let out a collective sigh of relief. The war was finally over. Tens of millions had died but it was over. Now comes the process of rebuilding everything that had been destroyed during the war. Keep in mind that the nature of urban combat along with the US dedication to strategic bombing of German (and to a lesser degree Japanese) war industries meant that the European industrial base was in absolute ruins. Literally. There was really only one nation that came out of the war with both its industry and population largely intact. The USA.
So while the economy did experience a dip immediately after WW2, it didn't last long. Investment capital absolutely poured into the USA and demand for industrial production was seemingly unlimited. Factories could reconfigure and retool for civilian production because the US was virtually the only nation capable of supplying industrial production. They enjoyed a virtual world monopoly (along with a few other minor nations like Sweden and Switzerland which also enjoyed significant upswings after the war). The effect was that the US economic boom was allowed to continue for decades after the war. Further fuel for the US economic boom was decades of unrealized domestic comsumption needs. The great depression and subsequent war meant that domestic consumption had been fairly modest for a long time. Rising wages, standards of living and the reconfiguration to a civilian economy meant that the US domestic consumption, particularly by the recently vastly expanded middle class, increased dramatically which further drove demand.
The TL;DR is basically this: Government spending and the war created a huge middle class, world and domestic demand in the post-war economic expansion allowed the US to pay for all the expenses incurred over the course of the war.
A small sidenote to all of this is that there was another nation that came out of the war swinging. The unlikeliest of fighters. Germany (and Austria). The German economy had been in stagnation for nearly 30 years leading up to WW2. Facing harsh reparations in the treaty of versailles and increasing economic isolation by the great colonial powers the Germany economy was on the brink of collapse in 1939. Part of the German economic goals of WW2 was to break the stranglehold the colonial powers had on Germany. In spite of the devestation and the obstacles to German innovation in the post war years (essentially, German industries were not allowed to keep secrets, even for intellectual property and patents, the allied nations could basically say "That's a nice invention you've got there. Yoink! It's mine now!" And they did exactly that).
Inadvertedly the war did almost exactly what Germany had hoped it would. It broke the back of the colonial nations. German economic isolation was over and with the rapid reconstruction of the Germany economy they really did become the continental hub of industrial capacity and trade originally envisioned. With the small caveat of losing the war and suffering catastrophic devestation in the process of course.