You can draw a line between Hitler's promises of a better economy and the war. Once in power he pumped millions into the arms industry and raised a larger army then was allowed under the Versailles treaty. Since you can't hold up the facade of a working economy by building up forces indefinitely (there's a point where your warehouses are full of ammunition and tanks are simply parked and gathering dust, and people will start wondering what the justification for all that is), he had to go to war. That simple. If WWII hadn't happened at all and Germany remained peaceful, its economy would have collapsed like a cardhouse.
You could say it's somewhat similar to the decline of the Soviet Union, wich started to weaken under the pressure of keeping up with America in the arms race, while the people saw little improvement in wealth over all these years and began questioning the system.

WW2 was really part deux of the first, and cannot be totally blamed on Hitler, but Hitler is of course responsible for the Shoah.
Good words, I agree totally.