How vast is Dominion space? You don't see any Borg present in the Gamma Quadrant. Does the Dominion control entire Gamma Quadrant? The Dominion were very hyper sensitive to any outsider entering their space. So I guesss any motive friendly or not is an act of war. The ferengi couldn't even make any serious profitable trading or selling in Quadrant.
I don't think the Dominion controlled the space immediately surrounding the Gamma Quadrant entrance to the Wormhole. Several maps and data displays seen throughout the series show the Dominion border some distance from the Wormhole.
The Dominion's decision to destroy any Alpha Quadrant excursion into the Gamma Quadrant would be similiar to the European Union deciding to destroy any United States excursion into the Mediterranean Sea. The EU doesn't control the entire Sea, there are other powers in the area, but they're definitely the big dog on the block.
As for what actually started the war, I believe it was the Dominion's attack on Deep Space Nine.