Question

When did military rulers take control in Japan?

Answer 1

There was never any formal take-over.  In any case, power was always theoretically exercised by the Emperor.  

Hideki Tojo was chosen by the Army as Minister of War and made Prime Minister by the politicians in 1941, a few months before the start of the war with the USA.  But Japan was already more or less committed, given the US economic sanctions following the war with China, which became a full war in 1937.

The Japanese system was actually one of weak government and an out-of-control army.  Army and Navy nominated their own Ministers and could prevent a government being formed by refusing to do so.  The army also did things like the take-over of Manchuria without permission from the government, which could not control them.  Most of the population preferred the military to the politicians, at least until the war started being visibly lost.

In addition, there were a whole series of right-wing fools who used assassination and one attempted coup bid to sabotage any policy that tried to moderate in the light of the actual limits of Japanese strength.  This is a common result of Hard Right policies, doing immense damage to the nation they intended to serve.

Japan could have avoided the main war by reaching a moderate settlement with China, where Chiang Kaishek had previously been willing to give away huge chunks of territory for the sake of being left free to pursue his war against the Chinese Communists.  But the same fools who prevented previous moderate policies would have probably killed anyone who had dared try it.  Meaning that the Japanese Empire was doomed, whereas it might have lasted in a very different future had they been less greedy and angry.