There is no real confirmation on who launched first and i doubt that there will ever be one.
And what does it matter in the end ? Such things were solely important to a world that ceased existing 200 years ago.
Fallout 3 put a bit too much of reference to the past into the game anyway.
Maybe the Washington location with all its museums and memorials is a explantion for why the people there keep a certain connection to the past with so much knowledge. But the west coast in F1 and F2 gives a rat's ass about the USA and China.
USA is nothing more than three meaningless letters to the people there. Most of them never heard of it anyway. Afterall ,what do they care ? They have their own factions and governments now. The past is the past and most dont have access to historic files anway. Who cares what argument your great great grandfather had with someone else.
Except for the Enclave, the USA aswell as China and propably the majority of countries from back in the days are long dead and buried since two centuries.
Nothing but dinosaur bones remains of them. The Enclave still holds to the past and dreams the fruitless dream of reversing everything back to where it once was.
Just like there is now a Italy in place of what was once the heart of a dozen times bigger Roman Empire. 2000 years ago now and nothing left except what you can see in museums today. Does Britain sue Italy for Roman occupation ?
Not really. What does it still matter after so much time right ? Wouldn't it be rediculous to start a argument about that ?
The Brotherhood knows about history but only cares for preserving and rediscovering technology rather than the old world itself. They kept no traditions of their U.S Army roots and replaced it with a medieval knighthood tradition propably as their founder was a deserter anyway.