The major factor that can bring these two superpowers into direct conflict is Taiwan.
The Chinese regime has constantly reiterated that within the next decade Taiwan will be integrated with the mainland, even if that is to be accomplished using coercion. 80% Of the Taiwan residents prefer the status quo, wherein they are not part of China.
In 2003 George Bush made unequivocally clear to the Chinse leadership that if China were to attack Taiwan, this would engender full scale military hostilities between the USA and China, because the the USA is committed by law to defend Taiwan against a Chinese invasion….
…How Likely Is A Military Confrontation Between The USA and China???
I forgot to mention that a Chinese general remarked a few years ago that if in the event the USA draws its missiles on Chinese territory, the Chinese will respond by nuclear weapons….