Probably pretty easy to type up a bunch of top secret bogus documents about dealings with aliens, and then just sit back and see who can't keep their mouth shut and who might be a security risk.
The universe is just too big, and too lousy with stars and planets for there not to be alien life somewhere. However, you've got to add onto that the odds that alien life evolves to sentience/sapience, tools, and technology. Evolution is a blind random process and doesn't have "goals". These final developments like we enjoy could be millions to one or even billions to one.
So even with trillions of planets in a galaxy, you could have millions of life bearing ones, but still have less than 1:1 odds of there being a technological species in any given galaxy.
And most people don't really get on a gut level what kind of technology it takes to do interstellar travel on an "at will" basis. If/when we take our first stabs at reaching the nearest stars, society, and what it means to be "human" will likely be unrecognizable to us today. Or Computers/AI/machines will be doing it for us. And those who know better tend to dumb it down by several orders of magnitude, like hard(er) SF authors, for the sake of having a plot, and understandable situations and motivations.
Interstellar travel tech implies insanely high technology throughout a civilization. "Fast" travel, if possible, implies control over the fabric of space-time itself. And "slow" travel still implies an insanely high level of technology because it implies scientific and engineering prowess that can make a ship and devices that can last for thousands of years and keep running.
The only realistic depiction of aliens to make it to a movie was probably 2001, where the inscrutable monoliths were an almost abstract extension of what remained of the technology of aliens who'd long disappeared into possibly some hyper-evolved abstraction themselves. And the Monoliths did their own thing for their own reasons. The monolith didn't show up at Area 51 and make secret deals with government officials.
Best we can tell, the monoliths plan was to give apes the idea to hit each other with rocks and bones. Then one hid on the moon to wait a few million years to see if that paid off, then another one orbited Jupiter to see if any of us made it that far.
Aliens that are enough like us to want to keep secrets, and make secret deals with governments to hide their existence from the wider population would be like you or I trying to sneak into an anthill and try to explain our existence to the queen, but ask that she not tell the workers. Problem is, the queen is still just an ant.
