Can the US annex China?
Never. Neither peacefully nor with violence can US annex China.
Why not peacefully?
For a state to be fully annexed by another, the people must accept tue fact that they're no longer in that state. But for China, consider this: there are 1.4 billion people in China. Only 10 percent officially received English courses, and about only 50 percent of them could understand and speak daily English. Then you have about another 50 percent of them being nationalists. I don't think there would be a lot of people who are willing to be apart of another country which they don't even speak the language there. So there would be only around 2.5 percent of the total Chinese population might be willing to become a part of US.
Then you have the Chinese Communist Party (the government) who is constantly telling you that China will become better than America, and the fact is that China is catching up pretty fast. So for the rest of the people there isn't much they're gonna have against their country.
Then you have internet censorship, which blocks pretty much anything up there against the CCP. So it's gonna be hard to spreak the word around like "if you don't revolt against the CCP then they will kill your family with a hammer and a sickle!".
So, no matter what happens, America can't persuade China to become a part of America. (I don't know about Mexico though... jks)