With the crippling of the German military after the Treaty of Versailles, the damage to the German men of working age from WW1 coming home (both dead and horribly injured), Hyperinflation in the 20's, the Great Depression and the collapse of the Weimar Republic in the early 30s... how did Hitler and Germany in general turn their economy around enough to be able to launch and support an enormous military campaign in 5 or 6 years, or by the end of the 30s?
Germany was always doing really well when wars were not going on. The normal state for Germany after 1870 was solid growth. That combined with the size and population would normally lead to Germany being 'dominant' in central Europe. Meaning they are the primary power economically and usually militarily as well.
The debt of Versailles was not crippling. You can have large debt and fast growth at the same time. After the Hyperinflation was resolved they again had good growth until the start of the Great Depression. Also because many reason, by the time Hitler came to power Versailles was dead in the water.
When Hitler came to power, the Great Depression was mostly over in most part of the world. Germany were hit particularly hard because of their refusal to devalue their currency, but even there the depression was fading. So had the normal state set in again, Germany was expected to have good growth again, and would soon 'dominate ' Europe economically again, the same as before WW1 (and now).
Instead of the normal slow evolutionary democratic politics, Hitler came to power and he was simply lucky that he was the outsider threw most of the Depression and then came to power, profiting greatly from the recovery.
In terms of growth Hitler did not 'turn the economy around' he simply shifted production towards military instead of civilian spending. He peacefully managed to extend the amount of people and production in his empire (Austria, Rheinland and the Sudetenland) and used as much as he could to boost his military power.
Most of the miracles of growth that the Nazis use in their propaganda are simple propaganda, highly exaggerated reports of how many jobs were created.
The Deluge: The Great War and the Remaking of Global Order 1916-1931
The Wages of Destruction: The Making and Breaking of the Nazi Economy
In addition to what has been said, Germany didn't have the economic power to sustain their military spending. Their military spending caused huge deficits and the war in fact was economically necessary for the state to survive economically. It's been argued that it got to a point before the war that Germany had to go to war to sustain itself as a state. There have been quite a few answers regarding Hitler's military spending undermining the state's financial solvency on this subreddit.