We had a vast amount of wealth built up after World War II, as we had developed a huge wartime industrial base. Since most other nations were either devastated to one degree or another by the war, or unaffected (no industrial base build-up), we were in an excellent position to export product. Thus we built a tremendous amount of wealth in American corporations and in personal accounts. As more and more of our goods and even services began to be imported, the foreign-owned corporations producing those goods and services built up wealth in American dollars. Many corporations and nations hold dollars as a form of wealth, but most of those dollars are traded for things that don't show up in the trade imbalance - American corporations (in the form of stocks, bonds, and mutual funds), American debt (T-bills and other government bonds), and American real estate. There are a huge amount of foreign-owned corporations that used to be American-owned; ditto with real estate. Companies that don't want to use their American dollars to buy American debt, real estate, or corporations can also trade their dollars to other companies that do.
It's like if you're working a very large family farm, busting your hump and clearing $40K a year. One day someone says "I noticed you have a lot of land, I'll give you $10,000 for this lot right here." So for that year your income climbs $10K and your standard of living goes up, even though your net worth goes down a bit (trading real property for transient personal property.) Do that a few years and you get to thinking that if you just sold two lots instead of one, then you could give up planting those marshy, not so productive acres and get down to a sixty hour work week. Then you get to thinking that if you sold a big chunk of land to an investor, you'd probably get enough to give up farming altogether and still make much more than you did farming, maybe just run some cattle on that land. It works pretty well, gives you a high standard of living with less work.
Until you run out of land to sell . . .