I think John J. Mearsheimer is actually quite hostile to China. He wants the war in Ukraine to end ASAP, so Russia can be united with the West in their opposition to their "common enemy" China. He can keep dreaming.
That is the most intelligent thing to do.
The Ukraine war is a masterstroke by China to fully sway Russia. Russia is an extremely valuable piece on the global board, potentially as impactful as all of the EU or even more so.
For every day the Ukraine war goes on, it causes an increasingly irreversible decline between Russia and the west. Russia might always be China's "ally", but the west can make Russia more useless to China just by engaging with it, much like how China is making India more useless to the west.
The smart thing to do was to throw the Donbass at Putin while the war was in an early stage. Putin might have set his eyes on full annexation anyways, but having an easy partial victory and peace would be heavy political pressure.
US' advantage over China is that they work better with corrupt politicians and subterfuge, which mainly work in peace, when emotions are cold and greedy people rule. While in war, hot heads, nationalists and principalists take over.
On the other hand, China's advantage is in hard power generated by sheer economic size and it's autarky, which lends itself well to conflict but not peace.
If I were US, I'd avoid conflict and use my media power and connections to oligarchs across the world to sneak up on China. I'd emphasize on and create signals of genuine equality in the US, in order to build bridges with Chinese and Russians, which will inevitably give me a lobby within these rivals. To Russians, I can appeal to our shared ancestry as white peoples. To Chinese, I can appeal that we are both rich and powerful nations that can work together on large projects to help humanity forward.
This way, I would create divisions. Using Hollywood and the UN to appeal to personal egos in their governments. In the long term, China's societal efficiency will decrease.
At the same time, I'd try to rejuvenate America's people as much as possible. Bring education to the forefront, clean up poor societal trends, rebuild infrastructure, so that I can innovate and build in America. Put a cap on rent seeking behavior and crack down on corruption. US is way too corrupt overall, but my elites would be allowed to be corrupt, as long as they also get results, while the ones that are corrupt and do nothing get axed.
Once I can build at least 1000+ cruise missiles a day like China and have my own DJI, I'd be more ready to assert my hard power. With all the tech and anti corruption drives, I might also have hit 6th gen fighters first and can surely make a lot more 5th gens than China can. And China in this scenario won't be fighting America with all they got, since they've been lulled in a false sense of security.
All I need to get global hegemony is then to squeeze China into becoming a perpetual yes man for me. And why wouldn't they? Unlike OTL, I'm not being especially offensive to China, and we're both rich, satisfied and have no land disputes. China is being increasingly societally weakened and financialized, while America has enough industry to put up more than a good fight. China has no reason here to oppose me if I decide to genocide some blacks or browns.