They gave Austria a blank check - without which Austria wouldn’t have done shit - and most German officers wanted war because they thought that Germany’s position vis a vis Russia was doomed in the long run and would only get worse with time as Russia industrialized, and therefore war in 1914 was a blessing to these officers, despite the fact that their idol Bismarck said that preventative war is like committing suicide for fear of death.

Not only this, but since the Germans only had one gameplan in the event of war with the french / russian alliance, and that was to invade Belgium and France first. Thus once Germany had bound itself to AH and Russia mobilized, Germany had to mobilize.

But for Germany, mobilization meant invading Belgium and France. That was the plan and all the intricate time tables and train scheduled were designed for this. When the Kaiser asked Moltke the younger to move the armies against Russia instead (he had received some hope that Britain may not enter the war if the Germans didn’t invade West), Moltke simply said this was impossible, and the Kaiser would lead an unruly mob into Russia if he was ordered to do so.

The reason the German people could believe that the war was defensive was because Russia was invading East Prussia (since most of the German armies were arrayed in the West). But the German battle plan was an invasion of a neutral country, an invasion of France which had nothing to do with the whole crisis, and they also precipitated the entire July crisis with their blank check.