Which SW Faction was the most powerful at ANY GIVEN TIME

Trade Federation- NO

Separatists- Droids were outsmarted by the superior creativity of clones, augmented by their separate Jedi. They lasted as long as they did because of their numbers, but mainly due to the manipulative skills of Dooku and Sidious, and their various apprentices. Additionally, bounty hunters and Nightsisters helped tremendously. Still, they were on the losing side of the war. NO

Rebellion- Death Star One just cost the Empire resources and denied them from blowing up planets. It also took out Tarkin, which could arguably be the biggest losses of Death Star One. Death Star 2 took out Vader and Palps, but still, it took longer to defeat the empire. There is also the case of Dumbass Imperial Syndrome in for example Star Wars Rebels, so we have to account for that. Still, Rebellion only won because it took the head off the snake, so....
NO

New Republic- You didn’t include this, but they weren’t well militarized anyway, so NO

Resistance- Again, the New Republic weren’t well militarized, so the Resistance was created. However, the highest members could pull strings in the New Republic and they were still pathetic. NO

First Order- The main problem here is that there were still some giant Star Destroyers after Sidious died. Idk. However, their power is diminished because if they had revealed the Final Order earlier, then the Destroyers would have survived and not been taken out by the lightning storm of Palps. Close, but NO

Republic- With the best of all factions against each other, Republic wins easily. Clones and Jedi individually take out all comers. The only thing that they wouldn’t win is best general, with Trench, Kalani, or Canon Thrawn in the lead. And Legends Thrawn wins that anyway, but you said no legends, and Thrawn isn’t even a Galactic Imperial, he’s Imperial Remnant. For example, Trench is a better general than Anakin. However, the clones are extremely versatile, which is what Anakin takes advantage of. So technically, while Trench is a better general using his commonplace troops, it is the versatility of the clones that gives Anakin the advantage. However, in a drawn out war, the Republic would lose to the Empire seeing as they have more troops and resources. NO

Empire- The big difference from the Separatists and the Empire was the skill of the troops. While the Separatists printed out about 1 Quintillion droids, the Empire only had about 1.1 billion stormtroopers on each Star Destroyer.
However, the empire had the perfect balance between skill and numbers, and they had Vader, Tarkin, and the machinations of Palps. Empire wins

 

the galactic empire was indeed really strong