The US wouldn't win a war against China anyway, not without great cost. They couldn't even beat the Taliban in Afghanistan after 15+ years, they've withdrawn and the Taliban are back running large parts of the country and having been doing that even before the US left.
They couldn't get Saddam the first time and couldn't win cleanly in Vietnam either. China is a whole other ball park of trouble.
I don't know about a "Cold War", but I think China has badly damaged their standing with the Western world, not just this COVID19 situation but other issues were already bubbling to the surface. I dunno about "Cold War" ... maybe "Lukewarm posturing", lol.
Those "wars" were won by the US militarily. Occupation is a different matter.
What comes after winning the initial wave of a war is part of the war. And the US would have no prayer of doing that to China, China is not some backwater military force, to engage them militarily straight up would incur loss of life unlike any war the US has ever been in (yes, WW2 included). China has a massive standing army with a shit ton of technology and a monstrous economy to fuel it with.
Even a so-called "Cold War" type of scenario is something the US probably has little stomach for.