Remember, Summerset's an island and the Empire doesn't have aircraft. Nazi Germany was able to invade France because the border wasn't as well fortified as the French believed, allowing German forces to go around them. Even then, they never really defeated France. The UK, on the other hand? Set on a collection of islands and defended by the greatest fleet in existence. German forces were only ever able to land a few troops on the islands and could only really hurt them with bombers. The Empire trying to invade Summerset would run into a very similar problem, but with the additional problem of not having bombers or any other aircraft to make raids. And that's not even getting into what a Thalmor destruction mage could do to a wooden Imperial ship.
As for invading Elsweyr or Valenwood, those are brutal environments that in real life have historically strongly favored the defending faction. It would be like trying to win both the Vietnam War and current war in the Middle East as the NATO/UN forces simultaneously. Even the Thalmor didn't invade and took them by coup instead. Meanwhile, the Dominion's Altmeri forces are still free to attack Hammerfell, High Rock, and Cyrodiil.
The only chance the Empire would have had would have been to bring in Argonia on their side. We don't know exactly what Argonian leadership looks like, but we do know they don't do much on that kind of scale without orders from the Hist or a direct personal threat, which the Thalmor did not represent.
Lastly, the war started just days or weeks after Titus Mede II was coronated. He had very little time to prepare and no Blades to provide intelligence since they were all dead or in hiding. We also don't really know how well the Empire is doing now since we've only seen Skyrim, but most of Cyrodiil was burned to the ground during the war and you really can't fight without basic infrastructure. That the Thalmor agreed to a treaty at all was a boneheaded move on their part.