No, that’s not quite exactly how they did it in the late 18th century.
Our own central government issued paper money ($241,552,780 in Continental currency) when the Continental Congress printed Continental Dollars from May 10, 1775 to January 14, 1779 during the Revolution.
By the end of the war, they had become worthless (“not worth a continental”) which left the colonists with a searing memory (read: a legitimate fear) of ‘printing money’.
Price stability depends less on whether money is issued by fiat (‘created out of thin air’) or fixed (with a convertibility rate ‘created out of thin air’) and more on the credibility of the fiscal and monetary authorities to manage the price stability of the economy’s money supply in a responsible manner.
To explain price instability leading to hyperinflation, you don’t need to go all the way to Wiemar, or Zimbabwe. Nor do you need to go all the way back in time, just look at what is happening right now in Turkey (a monetary sovereign, a net-importer, using a free-floating, non-convertible currency).