Bannon recommends an all-out economic war with China.
An all-out economic war between A and B make both A and B losers, and makes C to Z winners (which is why Russians like Kstatida will strongly support it!). People in the USA and in China will have to take economic damage in exchange for prolonging American hegemony. I think you could plausibly delay Chinese hegemony by some years, maybe move it from 30 years in the future to 40 years in the future, with unilateral economic sanctions, but at the same time the USA will also suffer.
I don't think the electorate as it stands today has this kind of appetite. Most voters care about their bread-and-butter, their jobs and their comfortable lives. To ask them to sacrifice their comforts in exchange for some vague notion of a prolonged American dominance is difficult. You'd have to actively lie to them and twist their minds with propaganda, and make them believe that China is out to kill them: this is a dangerous policy and can conceivably lead a democratic society on the path to initiating war against a non-aggressor target.
For reference, China isn't out to kill USA. They're out to slowly supplant the USA as the dominant economic player on the planet. Militarily, I don't see them trying to replace US security guarantees. They benefited strongly from US-provided maritime trade routes and security, they're happy to let the US continue to be policeman, as long as the police stay out of their backyard (East Asia). This is more or less the same as Russian policy towards USA. The only difference is that Russia is not a credible challenger for hegemon status, but China is. In that sense Bannon is correct to focus on China.
The really big disparity between China and the USA is human resources. China have more people, and their people are better.
What should the USA do instead, if it wants to really be on top?
Quite simple: an all-round change in culture and society.
(0) Change the culture. The cycles of civilizations can be pithily summed up as: "Hard times make strong people. Strong people bring good times. Good times make weak people. Weak people bring hard times." Of course there is much more involved, but this is a valid point. Americans are softer and lazier than they used to be. How many of you can honestly say you worked as hard as the average Chinese student in school, or the average Chinese worker at work? You may pity the Chinese their hard lives, but those "hard times" they suffered made them strong people. Hard work and discipline makes you happy, and gives you the capacity to achieve your goals. A happy and healthy society must revolve around a solid work ethic.
I'm actually doubtful that a democratic country can achieve a shift towards a more austere, hard-working culture. You'd probably need a war or something to unlock that famed steel that lies underneath the softness covering the modern American. No one is going to give the USA a war though, that would be stupid and suicidal on their part. The USA is like a giant tiger that's eaten its fill and is going to take a nap: why poke it?
(1) Raise the birth rate, especially of productive and contributing members of society. For various reasons, probably including genetics but certainly including upbringing, children of productive families have lower criminality, higher income, all the good things. You want to target a population of 600m, get close to half of China's. The rest of the shortfall can be made up with USA's vastly superior natural resources and geographical location.
(2) More immigration of talented migrants. This was the USA's secret weapon. Being anti-immigration is throwing away your secret sauce. The USA is an immigrant society, built primarily from migrants from Europe (white migrants). European migrants have integrated seamlessly into American society. You don't call yourselves German-Americans and Irish-Americans. You're all Americans. But this isn't often the case for non-white migrants.
2 (a) Become more welcoming to non-white talent. Talent happens in all populations, non-white as well as white. Welcome all talented migrants even if they're purple, or orangutans. As a talented non-white person myself, the disadvantages associated with being a minority are a significant barrier to my considering moving to the USA, and this is true for all talented migrants. Talented migrants live where they like, where they are welcome. They don't have to take shit from people. Being unwelcoming to other races means that talented non-white migrants won't come, but the untalented ones are desperate and don't give a shit. So you're skewing the migrant population towards being poor and uneducated. And this further raises racist and xenophobic tensions.
Some of you may claim that non-white migrants will still move to the USA because they don't have better alternatives: this is true only for certain non-white populations (I'm thinking Black, Hispanic, and probably South Asian) which do not have a reasonably-developed country to move to, in which they look similar to the racial majority, and whose language and customs they can easily adopt. East Asians can choose between Japan (if they can handle language/culture), Korea, tier-1 coastal cities in China, or Hong Kong or Singapore. South Asians can expect fairly decent (but still minority-status) treatment in Singapore, and I believe the UAE cities Dubai and Abu Dhabi are havens for talented South Asian expatriates where they have some degree of racial privilege.
2 (b) Related to the economic rivalry with China: become more welcoming to Chinese migrants. They are, on average, one of the most talented immigrant groups in the USA. Having to deal with discrimination and laws which make it hard for them to remain there drives many of them back to China. I personally know highly-skilled Chinese engineers and scientists who have gone back to work in tech companies in China (think Alibaba, Baidu, etc.) primarily because of the discrimination. If you can steal these highly talented people away from China, rather than driving them back to China, you can make huge gains in the economic rivalry.
Nation != Race. If you are a committed nationalist and want the USA to be the best nation it can be, you have to be race-blind. Every race has good and bad people. The best nation is inevitably one that steals good people from everyone and keeps out the bad.
The question is: can the American electorate swallow their pride and become better, less-racist people? I'm not confident that this can happen. So probably it is inevitable that China will win on the human resources front (larger population).
Notice that you have the option between (1) and (2). If it's (1), then make sure that educated, productive _white_ people are reproducing more, and talented overseas white migrants are brought in and turned into Americans. If the USA is a white country, and this is core to its identity and configuration, then you have no choice. You need more white people.
Some cynics might argue that the "racial minority tax" (the disadvantages of being a minority) will never be resolved. I'm almost inclined to agree with them, because I've not seen a society which has resolved it. If you strongly believe that the only solution is to go all-out white, then so be it. Keep the USA white. I guess this is the viewpoint of many on the white-nationalist right.