Another thought. The Federation arguably were armed enough to stand against the Dominion, because of the prep they did for the Borg.
The Q are officially neutral but Q put his finger on the scales just like he did in All Good Things.
The only way you can say Sisko was responsible for the war was finding the wormhole to begin with. The moment the Federation entered the GQ, nothing would have dissuaded the Founders from 'Bringing order' to the AQ.
No my argument is that since in "The Visitor" there was no war with the Dominion and the second time around when Sisko was rescued there was a war then Sisko must have played a decisive role in starting that war. It's not clear what role he's played, and it could simply be something close to the butterfly effect, but it was determining.