AH: The USSR never exists.

The best way to do that would be to keep the League of the Three Emperors intact and find a way to resolve the issues between Russia and AH in the Balkans. If the Germans can find a way to resolve those divisions and keep the League as a united bloc that would very neatly avert WWI. Revanchist France might be spitting mad at the Germans but they aren't stupid enough to pick a fight with Germany, AH, and Russia on their own.
 
The best way to do that would be to keep the League of the Three Emperors intact and find a way to resolve the issues between Russia and AH in the Balkans. If the Germans can find a way to resolve those divisions and keep the League as a united bloc that would very neatly avert WWI. Revanchist France might be spitting mad at the Germans but they aren't stupid enough to pick a fight with Germany, AH, and Russia on their own.

Easy in theory, near-impossible in practice.
 
Easy in theory, near-impossible in practice.

The only thing I can really think of that would make it plausible is if Pan-Slavicism embraces a more radical, rabidly anti-Austrian and anti-Russian stance than it did historically. If the Pan-Slavic movement ends up as something more subversive that would change how Russia reacts to it considerably, assuming it is possible for the movement to avoid co-option by the Tsars and other powerful European leaders.
 
OnkleWillie's The Twin Eagles and the Lion gives a possible route where Germany embraces Russia instead of Austria-Hungary, though it involves Bismarck manipulating things that results in the Russians turning to Germany for help, and also Italy gets a better trained army as well.
 
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