OK, for Austria to go against Germany, you could have a second Prussian-Austrian war break out. A trigger could be that time when Wilhelm II's Dachshunds went to Austria and ate Franz Ferdinand's priceless golden pheasants (closest thing to a war causing event I could find). It would be much more humiliating for Austria and have Prussia annex parts of Austria. That might persuade the Austro-Hungarians to ally with the British and the French, who are also looking to regain lost territory and honor. To put Russia on the German side, you could have Russian terrorists kill every possible member of the Tsar's royal family except the Kaiser or his close relative. That would allow the Kaiser or (did he have a brother, cousin of suitable age?) to take the Russian throne. With that close family relation, the Tsar uses his autocracy in much the way Peter III did, and allies with Prussia.
Then, when the war breaks out, the Archduke is dead, Austria attacks Serbia, Russia attacks Austria, France attacks Russia, Germany attacks France and invades Belgium, which gets Britain involved, and the Ottomans just go against the Austrians for Balkans territory.