Surely there was no reason to do that? Nobody was threatening the 3rd Reich in 1939.
First of all, despite 0% unemployment and high production, the German economy was facing big problems in 1939. In short these were caused by a plan economy that was focused on quick rearmament at all costs.
Now there are different schools of thought regarding the relation between these economic problems and the start of WWII. The British historian Timothy Mason argued that WWII started because Germany "fled to war" to steal and rob enough money to keep up German standards. Such theories were not without controversy (see for example Richard Overy).
Simply speaking, the controversy stems from the well documented intend of Hitler to go to war as quickly as possible. In effect Germany's economic position and employment rate were irrelevant to the decision to go to war.
Nobody was threatening the 3rd Reich in 1939.
Tell that to Hitler. It's a big question but there are a few issues here regarding Nazi intentions:
The first is that Germany in 1939 was a revisionist power. That is, its intentions were not merely the security of its borders but the very illegitimacy of these same borders, which had been imposed post-Versailles. Even Weimar governments had refused to accept the eastern borders as final (while accepting those in the west under the Locarno Treaty of 1925) but had attempted to revise them via peaceful means [1]. The Nazis had no such qualms. Within days of taking power (Feb 1933) Hitler had broached the subject of war with his generals and insisted on the absolute primacy of rearmament in budget discussions. He would subsequently go on to completely tear up Versailles in a programme of territorial expansion but right from the beginning Hitler was thinking in terms of war.
Secondly, this determination to rearm to revise Versailles brought its own tensions. Nazi Germany had relatively low unemployment precisely because the state was investing vast sums in rearmament. This however was not sustainable: it involved an inevitable clash with the consumer sector. Most obviously, the country's balance of payments suffered as investment was directed away export industries (needed to generate precious foreign cash) towards arms. The result was that the German economy spent five years walking an autarkic tightrope, trying to scrape together enough cash for the regime's need for massive military expenditures. It was a battle almost lost by 1938 (when cuts to major prestige projects were imminent) but Anschluss provided a temporary stay of execution. The Nazi quasi-war economy, regardless of employment rates, was not sustainable. It needed booty to sustain itself.
Finally, for now, all this was necessary because Hitler did consider the Reich to be under threat. It was opposed by the Judeo-Bolshevik and Judeo-Capitalist powers, threatened by jazz and other aspects of modern/American culture, its people at the risk of Volkstod (people or race death) due to a lack of 'living space'. Others followed him for various reasons but Hitler himself saw the world in terms of an apocalyptic racial struggle. (Which was of course not a novel idea in either Germany or the West – witness Grant's The Passing of the Great Race in the US, for example.) Peace in such a 'worldview' was just acceptance of a slower form of death. Kershaw writes that "The war for [Hitler] was no conventional military conflict. It represented the decisive step towards the fulfilment of his 'idea', the accomplishment of his 'mission'".
So why did Germany go to war? For a variety of reasons. Some were rational and some ideological but none mutually exclusive and all part of a toxic Nazi cocktail.
[1] In this Germany was pitted against the winners of the last war, France and Britain. As Britain's Admiral Chatfield candidly admitted in 1934, "We have got most of the world already, or the best parts of it, and we only want to keep what we have got and prevent others from taking it away from us". Germany was inevitably pitched against such a view.
[Edit: Sources