As a Libertarian and Austrian School guy, tariffs hurt the economy and hurt the tariff enactor more than the person whom you enact tariffs against

... assuming a free market otherwise exists on both sides

If you listen to what Trump's actually complaining about, he's basically saying he will use tariffs as a diplomatic weapon to remove the tariffs that have already been intentionally placed on us. Which would actually be a good thing if he can pull it off. That's not in the framing of this question.

Secondly, he's saying that he'd like to basically move back to a Gilded Age economic and tax system (which means massive de-regulation and de-taxation, replaced with tariffs for income). This would be a huge boon to the economy, as we currently exist in a Keynesian Socialist monetary system which is why the government is such a large share of the GDP. Trump's obsession with President McKinley suggests he wants that to be closer to 1% of the economy. The tariffs won't hurt us if we have a massive free market economy to balance against any problem they create, when our opponents will have massive command economy that won't be able to take advantage of our market.

Third, he is using to push back colonization. A foreign company operating in your borders is not a problem to most of the Chicago School because it comes with implicit assumptions like, "they will hire locals", and "they will be an independent entrepreneur". But these assumptions are false when dealing with Communists and Socialists. What we have seen so far, especially from China's Belt & Road Initiative in Africa is that all Chinese companies are in service to the Chinese Communist Party (no different from any other Socialists ever). The purpose of the corporation is not to make money, but to extend the power of the CCP. They will operate at a loss so long as the CCP can weaponize the lives of 1 billion people to extract all available wealth from and subsidize the corporation and it's operations in foreign territories. They can always out-compete to the detriment of their own economy so that they gain political power. They will hire predominantly chinese foreigners, settle them in the country, then use that colonial population as a political power base in the local government. If they do it a few more times, then they will do it in the state/provincial government. Unfortunately, China aren't the only ones doing this. You'll notice that the government is settling mass migrants in blocs of ethnic group. It's not random distributions, it's 20,000 Haitians in Springfield, OH; not a random aggregate. Having giant blocs of well placed colonies in the US not only guarantees extracted income from welfare that gets turned into remittances, but also political blocs of power within the US. Despite being a failed state, Somalia has a colony in Minnesota and a congresswoman who explicitly stated that her president is the president of Somalia. The point of some of these tariffs will be to stop colonization in the US which are using both American and foreign companies to create political revolution. Again, these are not hypotheses, it's already happened.

I'll put it like this: Thomas Sowell is a Chicago School economist who bitterly complained about Trump proposing tariffs before he was elected in 2016, and explicitly changed his mind on Trump because of how he actually did use tariffs. He changed his mind because he saw what Trump was actually doing. He wasn't having tariffs for the sake of having them because 'foreign product bad'. He was countering monetary aggression and building a gilded age economy. It might not be the perfect Chicago School style that he wanted, or the Austrian School style that I want, but it's a hell of a lot better than the SOCIALIST economy we currently have.