It's not built on faith but in authority. The reason the US can infinitely print money is because the dollar is the international reserve currency and the US imposed the dollar as the international reserve currency with military might.

Imagine there exist 100 dollars in the entire world. 50 dollars are in the US and the other 50 are in the rest of the world, the US has 50% and the rest of the world the other 50%. The US decides to print 25 dollars, now the world supply of dollars goes to 125. Now the US has 75 dollars and the rest of the world have 50 dollars, the US has 60% and the rest of the world has 40%. The value of each dollar goes down proportionally to the increase but guess what, the US doesn't feel the impact because it now has a bigger share of the money supply. Now add in that the demand in dollars is always increasing because international trade is always growing, unfortunately the value of the dollar is tied to the growth of international trade.

This is why dedollarization is an existential threat to the US, being able to print dollars infinitely and export the inflation has been their free lunch since WW2. When countries stop using the dollar for international trade, the dollar stops strengthening proportionally to the trade of said country, and when that happens the US finally feels the consequences of printing money.