I read a book on it years ago, must be about 15-20 years ago now. There was a series about the Enterprise during the Dominion War, I recall Riker saying they spent a ton of time repairing the Enterprise after it was half Borgified. They were deployed on various missions, if I recall one involved destroying a Dominion Superweapon? It has been a long ass time. If you want canon explanations, the only time we see the Enterprise-E in that period is Insurrection. There it was on a diplomatic mission, there is no reason why Starfleet wouldn't also continue diplomatic efforts to support the war effort against the Dominion and Picard is a first class diplomat. I also recall the Son'a having supplies of Ketracel White? So Starfleet would have been trying to keep them on side. What we see in Insurrection was part of the war, it might not have been a fleet battle, but it was important. They're also trying to research the Baku and the healing energy of the planet - that could be related to the Dominon War to give an edge to Federation or Klingon ground troops. First Contact took place a few months before war broke out, you can head canon a bunch of shit as to why they were not involved in the early Dominion War - the Enterprise-E was full of Borg technology, it was badly damaged and would have missed the opening war and certainly Operation Return. Alternatively, the Enterprise-E was active, but wasn't part of a fleet because it was the most powerful and advanced ship, so it was able to take on more dangerous missions. It simply was in the same position as the Klingons or the Starfleet ships that didn't make it to the battle.