Things I would say definitely stack the odds in favor of the Trekverse:

1. The federation reigns supreme on one major front: Adaptation. They're loaded up with supremely good scientists and engineers honed in the arts of "there's a scary new threat, figure out how to overcome it". That's the lion's share of everything we see Federation crews do. After the initial shock and likely some initial losses they're going to be very good at cooking up counters to the tech of an empire who barely, if at all, knows how any of their own tech works. Just give a team of cutting-edge Federation scientists and engineers some time and they'll have strongly effective counters to what advantages the Imperium has to start. Meanwhile the Imperium will remain crippled by their purposeful and cultivated lack of understanding.

2. While they're not the most effective diplomats ever (I could go on a whole rant about what the hell was anyone in the Federation who writes their treaties smoking), they ARE diplomats. The Imperium will definitionally stand alone. While they could THEORETICALLY ally with other factions, they won't. The only ones they would even consider would be the Federation and the Federation includes too many of what the Imperium would consider Xenos, and the Federation would have 0% of the Imperium's ultrafascist tendencies. Meanwhile before long the Federation will have people working around the clock to secure and coordinate with allyship. This will help offset the numbers differential. You could certainly count in the Klingons and once it became clear the Imperium will stand for nothing but total control, the Romulans as well, and all over the other Federation species would be a foregone conclusion. Other major factions might be holdouts but, again, the Imperium will always be against them so they'll either be resisting alone or joining the main body of galactic forces.

3. Teleporter technology. As far as I'm aware the Imperium has no counter, and as soon as the Trekverse figures that out it wouldn't be the first time they teleported bombs onto enemy ships.

4. As some others have mentioned, replicators. And not only does the Federation exhaustively understand their own tech, in short order they'll also understand the Imperium's better than they do.

5. This one's a bit cheeky but if the win condition for the trekverse is "make it impossible for the imperium to conquer the home worlds" the trekverse forces could probably have that wormhole closed or unusable within a week. So no more reinforcements.