Relatively minimal in this case basically means the President issuing orders and various US military platforms doing relatively routine things to carry those orders out.
Fundamentally, a modern nation requires electricity. It requires telecommunications. It requires gasoline and diesel. It requires a whole host of industrial and transport infrastructure.
All of those things are relatively time intensive and expensive to build, are generally not fortified, are fixed targets, and can't be replaced rapidly or easily.
Take France for example, it has less than 90 nuclear power plants. Even if you decide not to target the nuke plants it is fairly trivial to target the high tension power lines that move power from those plants to everywhere else, and just as easy to target the substations and transformers that are needed to get that power to the end users. Seriously, take out a few hundred targets and France goes (generally) dark for weeks to months even if you do nothing else. With sustained effort you can make it effectively impossible to get repairs done basically ever. Most nations have (at best) a handful of ports that are able to accept cargo at scale and a hand full of critical rail lines. Put a bunker buster into a mountain pass, for example, and you can shut down the rail line that goes through that pass for weeks to months. Or take out a few bridges. Hit the major off loading facilities and infrastructure at a port (a relative handful of cranes, for example) and you can cut a nations ability to import anything by at least 90% basically instantly and that will be the case for months.
Drop bunker busters on the right locations and you can cut the water mains into a city and essentially cut off municipal water to an entire metro area for days to weeks.
For most nations, the internet can be taken down with strikes on a few critical nodes. Or at least degraded to an incredible degree.
Now do all of this in coordination with the use of large scale cyberwarfare. What is essentially ransomware hitting basically every connected computer system in the nation, for example.
And in coordination with the US Navy notifying the world that the USN will sink any vessel traveling too or from the targeted nations ports and shooting down any airplane flying in that nations air space.
Simultaneous with all of this are the precision guided munitions targeted on essentially every potential unity figure in the nation. Securing El Presidente might be a bit hard but dropping bombs on the bedrooms of basically every Deputy X, Colonel, Mayor, Police Chief, business leader, etc. at 3 AM local and in coordination with the infrastructure strikes? That's fairly trivial and it destroys any real hope of coordination or unity.
Ending the ability of a government to exercise control over its territory and preventing the ability of any kind of large scale coordination is fairly trivial. And then you just wait while putting up what is effectively a blockade and dropping a bomb on anything that looks like it might be a good target. After that you wait a month or so for civilizational collapse to take care of the problem nation for you.
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It's like the China problem. The US doesn't need to send a single ground troop into China to destroy its ability to survive. The US already knows the location of basically every power plant, transportation hub, and factory in the entire nation. The USN captures or sinks every ocean going vessel moving too or from China, which basically instantly cuts off essentially all of the raw materials needed to keep China alive. The power in every major city in China goes out. And then the US waits while lobbing cruise missiles at factory after factory in a steady cadence. If China goes nuclear then the US also does and the Chinese population drops to under a hundred or so million in about an hour. If China doesn't go nuclear then the government has to focus all of its bandwidth on internal stabilization and its own survival while China has also ceased to be of any great relevance on the world stage.
Global depression? Sure. For a year or two while the US builds out its industrial plant on a crash priority, wartime, basis and then things are mostly resolved.
Geopolitical consequences? Well yes, the US did just basically end one of the worlds great nations with relatively trivial ease. But then, for the US those consequences are again relatively light.
The US can't properly conquer, occupy, or integrate most any nation in the world and certainly not rapidly. But conquest and occupation are very different from neutralization and destruction.
And if Europe really wants to replace the US it needs that level of capability.