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War cannot simply be waged on a whim, "Before troops and horses move, provisions must go first; before war begins, diplomacy leads the way."
The political landscape of multiple states existing on the European Continent dictates the importance of diplomacy.
The Vienna Government did not yet have the confidence to confront all European countries at once, which is where the role of diplomacy became prominent.
It wasn't necessary for all countries to support Austria in starting this war, but it was crucial to ensure that at least the majority did not oppose it.
Smaller countries were of less concern, mostly being opportunists. To them, Austria was already powerful; a bit more strength wouldn't matter much.
As long as their own interests were not harmed, they would, at most, voice some dissatisfaction.