Proof of aliens wouldn’t be your typical info that requires clearance, it would be the highest level of compartmented info. Everyone involved would need the highest security clearance. Everyone. Whoever empties the garbage cans needs to be trusted.
This wouldn’t be like nuclear secrets or spy secrets. All you need is one or two people who believe that disclosure of aliens would benefit humanity more than the secret will protect them. You need one Edward Snowden for aliens - someone reputable to blow the whistle with hard proof of some sort.
The amount of people that would need to keep this secret forever is astronomical. Not just the people directly involved, but any second or third degree contacts who find out would also have to keep the secret.
The ability to maintain a secret is an inverse-square function. The more people, the longer time passes, and the less involved they are day-to-day, the more likely the security will break down. There would absolutely be deathbed confessions. Over time, the probability of disclosure happening increases towards 100%.
This is why most conspiracy theories don’t hold water. No secret can last forever and certainly not one that big.