If we are keeping it within the time frame of right when Origins begins to when Trespasser ends... I would think telling Duncan immediately about the Architect and his awakening of Urthemiel would be the greatest change. The Wardens know where the Old Gods are and Duncan knows about the Architect, so there wouldn't be too much confusion.
That could possibly help stop the Fifth Blight from even starting... if they stopped the Architect in time... which would make everything change.
No Hero of Fereldan, no mass exodus of refugees, no Hawke in Kirkwall, no Anders becoming a warden, no death of King Cailan, Fereldan would remain strong, the events of Legacy would not have played out as they did if at all, Cory would probably still be imprisoned, Morrigan probably wouldn't leave the swamp...
and Solas would probably have no one getting in his way to bring down the Veil since there would be no need for an Inquisition in 9:40 Dragon.
Edit: I mean telling Duncan right when the opening scene begins, before we even go to whoever the player chose to play. If Urthemiel already woke up, at least they would get more Wardens involved and be more prepared... maybe...
Yeah, this would be a big one.
There is one major question: can the thralls of Corypheus reach Hawke? I assume Ferelden is quite a distance to track down the family, when you're starting in the Vimmarks. But that's assuming none of the Hawkes visit the area their family originally came from. Sure, now all ties are severed, but a few years down the line they might wander there to... I don't know, bury Gamlen or something.
Also, with all three Hawke siblings now surviving, there's an increased risk that one of them will have children, who will also carry Malcolm's blood. If any of their descendants have reasons to visit the Free Marches, there might be insane Corydwarves waiting at the gate.
Aside: can I just interject what a terrible plan it was for the Wardens to seal Cory using the blood of someone with a family? I get that it made him easier to manipulate, but exponential growth says that if his children survive and have kids, in a few generations there will be a huge population of people that can unseal the prison. It would have been much safer to recruit someone with no (heh) legacy. Or better yet, a childless, postmenopausal woman.
Though I guess given Cory's influence on Wardens, that kind of subtle stupidity may not have been an accident.