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Indeed, even in the 20s the Reichswehr already took covert rearmament measures. Hitler just amplified the process. The Versailles powers would rather have their defeated enemies remain in the defeated status forever, but a return to normality implied Germany rearming to some extent. It's like what you've said of Hungary and the Trianon states.
What made Hitler's military buildup bellicose, according to Tooze, was the nature of military spending itself, civilian gains forfeited by rearmament, the willingness to risk recovery altogether for the sake of the Wehrmacht and Hitler's strategic views on war.
Germany didn't pursue a double-barred recovery with vigorous civilian and military growth not because it didn't want to, but because it couldn't have both. Imports were severely restricted, so Hitler had the choice of importing for civilian industries or the military-industrial complex, and he chose the latter. Hence the textile industry stagnated. Under the import rationing system, some industries would have to starve, and he chose to starve textiles to feed weapons.
While talking of rearmament he mentions the usual opinion of economists about the arms industry: that it's a dead end, a money sink, whose final products aren't used to further develop the economy. And yet this doesn't hold true for the 30s Wehrmacht, which improved national prestige and made Germans happier. More than that, it was an investment which would be paid back in the future.
How an investment? Hitler didn't believe that peaceful capitalist development could save German geopolitics and provide a high standard of living, as Germany lacked means of sustenance and competition in world markets would lead to another defeat by Britain and its allies. Ultimately those aims could only be successful after scores were settled with Germany's enemies in a war. Such a war would inevitably happen, though not in 1939, as rearmament plans expected full preparedness by the 1940s and the Kriegsmarine would only be ready by the very end of the 40s.
The NSDAP's agrarian constituency also believed military expansionism was necessary to secure good living conditions in the countryside, and as I'll write later they had good reasons for thinking this.
Despite this funneling of resources to the military and the "money sink" nature of military spending, it employed many workers, created demand for the factories and carried along the recovery. The problem is that by the late 30s military expansion was going so fast it now contradicted rather than spearheaded economic recovery. The carefully built trade system and administrative controls were suffering under the strain. The regime's economists, such as Schacht, now advocated that rearmament should proceed at a slower pace to preserve the economy, but Hitler rejected them. One must conclude he was using his "economic miracle" as a means to achieve rearmament rather than the other way around.