This Picture Is North Korea, China, Iran and Russia's Worst Military Nightmare

Excellent picture share brother.

I have always wondered if our fighters will establish air superiority. It would be a big step in winning a conventional war.

I don't think the Russians or Chinese want to go toe to toe with the USA in the air... so they won't. China would concentrate on knocking out carriers and Air Force staging locations in Guam, PI, and Okinawa. Russia would employ means to make our smart weapons miss through GPS spoofing and try to turn our lights out with a cyber attack and paralyze leadership with a robust disinformation campaign.
Both countries are quite capable of doing those things.

Apples to apples, we would eat their lunch. A SINGLE aircraft carrier wing could take on the PLA Air Force and beat it dramatically. They'd have to be cagey about it until they reduced China's surface to surface missiles and air defenses, but then it would be a smoke show, limited only by ammunition and pilot endurance. There is a lot of them, and they are catching up, but the Chinese simply can't match us in the air with the US having marked advantage in hardware, training, experience, and tactics.
So they would go another route to gain their objectives.