It is in fact an interesting question, and I think it deserves a couple of answer not to be found in common economic theories.
First of all one should distinguish between pre-war and war time nazi Germany. For example there was in enourmous rise in US GDP during the war, though hardly anyone would consider these “good years”. Huge public weapon procurement programs do hardly compare to common economic activity. And surely that is one part of the answer..
It has been noted already, that germans stopped reparation paymens that were a huge burden to their economy before. And it is also correct, that this can not be precisely owed to the nazis, but the overall rise of nationalism and rebellion against allied policies certainly contributed.
It is not true, that the economic build up till 1939 was only due to massive government spending. In fact public debt was relatively stable, and of course sharply down with respect to reparations.
A part of public funding however came from the confiscation of jewish property, and that of course goes well beyond “economic policies”. However, on other occasions, “land reforms”, which frequently went along with confiscations, had also shown positive effects on economic growth.
But the most important “nazi achievement” was probably an overall mobilisation of people. They had 100.000s of NSDAP members working for free, building roads, doing social stuff .. whatever. They fought unions and eventually made them illegal. The “master race” was a hard working one as well. Demanding hard work was widely accepted, as economic progress was evident and fears were rather bound to joblessness and poverty. The overall optimism in pre war nazi Germany was also evident in birth rates.
If one could inject such kind of optimism into a democratic society, then for sure there would be some lessons to learn at this point. And maybe programs like “new deal” did just that, without being specifically usefull with regard to their explicit economic effects. The concept would be to make market participant more flexibel in their price expectations, thus solving a lot of issues with sticky prices while encouraging investment…
Anyway, war time Germany was a different story again. Specifically in the early years, despite the huge resources gained, german arms production remained at a relatively low level. The nazis thought they had already won the war and had put (too) little effort into producing more arms. It was only in 1943 that they eventually cought up with the pace of allies and soviets, at that time however it was already too late.