I am not sure that I will be able to answer your question to your satisfaction but I will at least try to discuss a number of misconceptions that need to be dispelled to gain any understanding of the modern economy.
Tangible consumer products are only a small part of the economy. The US (or, for that matter, Germany) also produces a lot of things you will never see in your home or backyard. Machines, military equipment, legal or financial services or even cattle fodder (one thing the US not only produces but also exports).
Incidentally, you wrote somewhere that military spending is “only” 5% of the GDP. It sounds like a lot to me and at the end of the day, US production is going to be the sum of all these “small” sectors. Unlike some other countries, it's certainly true that the US is not dominated by one or two narrowly defined sectors so there is no “one thing” the US produces above all else.
Brand and production are largely disconnected and added-value can be distributed in many ways. Your very first example is your car, which you claim is made in Germany. But the truth is that car makers just about anywhere assemble parts produced in various places, either directly by themselves or by other companies (maybe not in China and India but certainly in mature economies, including Germany).
Supply chains in this industry tend to be particularly complex but it's almost certainly untrue that your car is entirely made in Germany. Meanwhile, French factory workers go on strike against French car companies moving more and more activities to other places in Europe like Romania and Toyota advertises the Yaris as a car “made in France”. It's just way more complicated than the name on the product might suggest.
More cogently, all major German car makers actually have plants in the US, producing for the US market. Much of the value is arguably provided by R&D workers and most of the profits are presumably captured by management and shareholders back in Germany but in terms of production, it's also happening in the US. So “German” cars is one thing the US produces.
Exports are another question entirely. I first thought you were located in the US and then realized you were not, which means most US-based services are not available to you and any US products you might own would have been imported. Now, why would you expect that the US necessarily exports something you might want and/or can afford? In principle, it is entirely possible for the country to produce a lot of things and be richer than any other country on earth without exporting anything at all.
As another, completely different example, let's consider the Soviet Union and its satellite states. They exported virtually no recognizable consumer products to the West and had a lot of difficulties being competitive or getting what they needed from the global market but they still produced something. In spite of all its problems, the SU industrialized Russia and became much more productive than traditional non-industrialized societies. Given its (relatively) large population, it did in fact produce quite a lot and manage to hold an arms race with the US for a few decades (before ultimately collapsing, obviously).
Now, in reality, the most successful economies are embedded in international trade and export and import many things but they also mostly produce for themselves. How this works out is a complex question in itself but there is no need for the US to produce your car for it to be rich and produce many things.
Finally, the balance of trade is yet another thing and it's closely connected to currency exchange rates. The US does export many things (not necessarily to China) but that does not mean it will have a trade surplus. In fact, the US has a large trade deficit but that's not because it does not export anything, let alone because it does not produce anything, that's mostly because China holds large amounts of dollars and keeps its products cheap that way.
Germany is a mirror example. Its economy has many problems, it has not seen any impressive growth or productivity gains of late but it's still quite successful at exporting some high-end tech products and because its main trading partners are locked in the euro, it can easily maintain a large trade surplus. None of this is directly connected to the size of the economy as a whole or the wealth of the country.
And as a matter of fact, as @DVK remarked in a comment, the US does still produce many cars, only for itself. So products for local consumption (including food!) would be another part of what the US produces, and quite efficiently so.
Services are a major part of mature economies. In the US and a bunch of rich European countries, somewhere between 70 and 80% of GDP. In Germany, it's 71%. Why that is and what that means is also a complex matter but you cannot completely ignore services (like you did in your question) and say anything meaningful about the US economy.
These services come in several guises. Some of them (legal or financial services, business consulting, etc.) are actually high-value services that the US exports. You dismissed Hollywood and software but those are not negligible either. Even if you are not personally seeing any of it, all this is part of what the country produces.
Other services might seem completely unremarkable to you. It's a well-known and quite interesting fact that even low-productivity sectors see an increase in wages as the economy as a whole gains in productivity. So hairdressers and sale clerks in the US might not be doing anything special but they sell their services for a higher price and they have a lot of purchasing power compared to people elsewhere in the world, just because they do what they do in a rich country.
You remarked somewhere that it seems that many US people are simply selling and reselling goods produced elsewhere and to an extent, it's completely true not only of the US but also of all other advanced economies (but they are also cleaning, cooking meals and selling houses). Furthermore, because these sectors are labor-intensive and have a low productivity, they represent an even bigger share of the workforce.
As a though experiment, imagine that soon robots will completely replace factory workers (something many people have been announcing for some time). Obviously distribution and ownership could be a problem but, as far as the economy as a whole is concerned, we would all be extremely rich without anybody doing any of the production. We could all pay each other to do seemingly simple services (which would become more valuable than manufactured goods which would then be plentiful) or maybe not do anything at all and still have a lot of the things produced by the robots.
In fact, it's an expected result of productivity gains in other sectors and it's a good thing. A lasting split between a competitive export-oriented sector and lack of growth elsewhere is a major problem in some countries (it was a concern in Ireland for example or in countries exporting valuable raw materials). A minority might be able to enjoy imported products and cheap services from the rest of the population but most will remain poor and the country is hugely dependent on the vagaries of international markets.
You might never set foot in a US fast-food and think that massages in Thailand are better but it's still a fact that none of the richest, most productive economies in the world are export powerhouses centered on manufactured goods or heavy industry (although one of the biggest, China, is, see below for more). Incidentally, full-time domestic servants, the most exclusive type of service you can imagine is common in poorly performing, highly unequal countries but virtually inexistent in mature economies.
All this might sound counterintuitive and anticlimactic but it's a fact that low-productivity services that have to be sourced locally are a large part of what the US currently produces. And because other sectors (from agriculture up) are extremely productive, those services are valued higher and everybody can be richer than in an economy without such productivity.
There are a few other things that makes the US seem richer but might not reflect any actual structural difference. For example, US workers tend to work more (over their lifetime) than, e.g., Europeans. Because of that they do produce more “stuff” (to quote a recent advertisement) that shows up in the GDP calculation but they have less time available for other endeavors.
By contrast, what makes both Europe and the US much richer than they were a few centuries ago is increased productivity. 300 years ago a shoemaker could make perhaps a few pairs of shoes a day. Now a handful of workers with the right machines can make thousands of pairs of shoes. We can choose to use this increased productivity to have more shoes or to have more free time while still having the same number of shoes but we are much richer in any case.
Another thing is that domestic production is difficult to account for in the GDP. If you cut your family's hair, there is no monetary transaction involved. If a state hairdresser cuts hair for free, you can't easily put a price on that either (OK, I don't know if there ever was something like that). Statisticians do have a few tricks to take those things into account but it's not a perfect science.
To the extent that the US went further than Europe in moving some things outside the realm of domestic production and to the private sector (eating out at McDonald's compared to cooking at home to use a cliché), it could have a seemingly higher GDP while producing essentially the same thing (e.g. a meal).
US healthcare, in particular, is a bit like that. It's good but it is extremely expensive compared to healthcare in similar countries with no obvious benefits in terms of outcomes (you can cherry pick a few statistics to make it look better but there are really no large differences, e.g. in life expectancy). And it does appear in national statistics at the level it is paid for so that is a not-insignificant part of what the US “produces”.
Finally, don't forget that the US is big (and China is even bigger). You mentioned GDP (not GDP per capita, purchasing power parity, productivity or whatever but just GDP). One factor behind it is obviously population size. There are a few countries that might be richer than the US on a per capita basis and quite a few that are only slightly poorer but all those that come close are smaller in terms of population. In total, the US also produces a lot because it is simply bigger (the EU is keen on lumping all its member states together to produce impressive stats but those are still independent countries).
But China has or is going to take over no matter what. You might debate the details of its statistics or the exchange rate, it might face a serious crisis at some point in the future and it's still much poorer than the US, Japan or Western Europe on a per capita basis in any case but it is mind-bogglingly huge. And so it already has a very large GDP. That's all it takes to be the world's first economy.
