Nope. The gov cannot keep a secret, no one can.
In 1985, I worked with an AF OSI officer who was to conduct a routine phone screen, listening to phone calls of people at the highly secret NSA/NRO facility in Denver (search: “Aerospace Data Facility”). Within 2 hours, all major secrets were stated over the phone. Within 2 days, 100% of all classified secrets were stated over the phone. Routinely, and often.
In other words, there really are no secrets. We just pretend and the other side pretends, but both sides know everything. It is simply far too easy to know. BTW, a few years later, it came out publicly that the Soviets had tapped those same phone lines in the streets of Denver. They knew everything.
So, no, the government cannot, and could not, keep such a thing secret.
Governments can't keep secrets from other governments but you can safely bet that they all keep secrets from the rest of us.
My favorite counter-example to those who claim “government cannot keep a secret” is this incident that had zero whistleblowers ever:
https://www.scientificamerican.com/article/confirmed-the-us-census-b/
The only reason we know about it today is that some scholars were digging in dusty archives and bumped into it by accident.
Btw—governments spend billions of dollars trying to keep all kinds of military and intelligence secrets.
If there is “no way to keep a secret” then they should just declassify everything and save a ton of time and money.
Please explain this to all the intelligence agencies of governments and even corporations around the world.
How many trillions of dollars have they wasted to trying to keep secrets they could never possibly keep?
Lol.