In an economics class many years ago, I asked the exact same question as the OP. I don’t know what exactly the professor said, but it was something to the effect of, “Even if you printed the money in secrecy, somehow it would still affect prices anyway.”
I think it boils down to if the printed money reaches the economy in any way, it tends to cause inflation.
Yes, if the money ends up in the hands of consumers, then you have more money chasing the same number of goods. Inventory gets cleared out in a hurry, and then stores find they cannot resupply unless they bid higher than other stores. Or, suppliers respond to increased cost in raw material by raising their own prices to protect their own margins.
Once the money gets in people’s pockets, they are going to go out and spend it. And businesses are going to notice that their goods and services are being sold more quickly, and raise prices accordingly.
Inflation can be caused by any process that destroys the balance between money and goods. When Spain brought massive amounts of silver back from the new world, but didn’t increase its supply of goods the result was also massive inflation. Even though silver is not printed money. Of course a lot of it went to imports from other countries, but only a few people controlled all that silver so the inflation destroyed the economy for the rest.
Right. I read one historian explained it as Spain had more Money, but not more Wealth.
Money is fungible. Any money in any form can be converted into an equal amount of money in any other form. Sounds tautologically basic, but in this example it means that once money is created no one can tell it from all the other money out there. Money therefore cannot be hidden. Hidden money would have no value at all. Money is designed to be spent. If a pallet full of money sits and never is found, then it does exactly nothing to the economy. Money spent in any form does.
Right, I almost mentioned that myself, and was reading about it here. Interestingly, the inflation in question was only about 1.2% compounded, which by modern standards is relatively low, but high both for the time and considering the monetary and economic policy in the 16th century.
Basically Spain made little or no effort to invest in the country and increase the goods and services produced. Instead they mostly spent the silver on foreign goods and Habsburg war efforts.
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As satirized in Candide when the title character acquires massive quantities of diamonds from El Dorado (where the natives consider them “worthless pebbles”) but ends up impoverished anyway.
Is OP implying that “covert” money creation doesn’t cause inflation while “overt” money creation does?
I’m not sure what the argument is about. Small amounts of money are … small. The USG is already spending an extra billion here, billion there for non-productive uses. Friendly banks happily create the new money, if the interest rate is high enough.
FedRes HAS been creating money without advertising it (i.e. buying bonds with no announcement), but the actions are in the public record. Opposite to OP’s suggestion, if it tried to keep this money creation secret, that would come out and the resultant panic might trigger a sudden drop in dollar valuation.
Well, I learned a lot from this thread. It turns out that the answer is much more complex than I expected it would be, ultimately, and all the more reason why I’m glad I didn’t just go to the chatbot. It also vindicates my not being able to make head nor tail of it all these years. 
If your printed money has an effect, then it has an effect. If you print money and bury it, then it won’t cause inflation, but it won’t accomplish anything else, either, like paying off debts or buying stuff or whatever. But if you do do something with it, like paying off debts or buying stuff, then that act itself is the mechanism by which it causes inflation.
As Chronos implies, it is a fallacy to think price level is directly proportional to money supply. In fact a classic equation of monetary theory is
. . . . P = M × V ÷ Q
showing the Price level as equal to the Money supply times the Velocity of money divided by Q, where Q is GDP or some other macroeconomic total. (Cf. Velocity of money - Wikipedia )
If $100 is injected into a small town where people immediately spend the money as soon as they get it, V might be several transactions per day, and several demand curves might be pushed up (supply × demand curves controlling prices). On the other hand, big banks have gigantic reserve accounts at FedRes that sit with velocity zero (thus having no direct effect on price levels) And in fact, increases in M often lead immediately to decreases in V.
Those gigantic reserve accounts, paying 3.9% interest at present) were an innovation to avoid a repeat of liquidity shortfalls in 2008. (The interest paid by Fed to the Member Banks holding these reserves led to FedRes suffering a net $114 billion loss in 2023.)