The only chance I can see for the Feds to win on their own is if they mined the wormhole immediately after the attempt to blow up Bajor's sun. I'd question whether the Dominion or the Cardassians would really be ready to prosecute a war at that point. Sure they kicked the Klingons out, but there is a good chance the Klingons were not ready for high intensity conflict (or maybe even knew the Jem'Hadar were there is force) and it is possible their shields didn't work against Dominion weapons either.
Actually, that might be an issue for the Feds to at that point. Given Weyoun's surprise in "Call to Arms" and the fact that Federation ships are "disappearing" on patrol of the Cardassian border an episode before in "In the Cards" it might be that the shield breakthrough didn't happen until "Call to Arms" or just before it. You can have all the Defiants crewed by holograms or AI computers but if they can't take a hit they are worthless.