As others have stated, the existence of extra-terrestrial life seems a near certainty. We know that intelligent life can evolve in the universe (QED: we exist) and given the vastness of the observable universe it seems highly probable that it's happened more than once. Limiting ourselves to just the Milky Way galaxy, again given the size and number of stars, it seems reasonably likely that there is other intelligent life here.

Have they been to Earth? This one strikes me as less likely. The universe is big, just mind bogglingly big. Even an infinitesimally small part of it, like the Milky Way galaxy is still insanely big. And as best as our current understanding of physics provides, we cannot exceed the speed of light. And even trying to approach that speed is fraught with all kinds of problems. At any significant fraction of the speed of light, bumping into tiny bits of space dust can cause real problems for spaceships (think: nuclear weapon level energies released). Even sub-atomic particles cause problems, as they will be the same as high energy radiation at those speeds. Even if those issues can be handled, there is the problem of reaction mass to get ships up to and decelerate from those speeds. Even electric ion engines need some sort of reaction mass to push against, and that has to be carried. This then runs us face first into the Tyranny of the Rocket Equation. For every extra bit of reaction mass you carry, you need even more reaction mass to get everything up to speed. Eventually, you're trying to carry so much mass that the whole thing just gets unfeasible. As a related tanget this XKCD What-If gets into a lot of the same issues.

So ya, I doubt that ET has been to Earth, simply because crossing the gulf of intergalactic space would require an investment of resources which is so insanely big that no sane species would bother. And then there is the whole issue of time. Sure, at a sufficient speed and thanks to Lorentz Contraction you can actually cross the Milky Way galaxy in a reasonable amount of time, in your own frame of reference. IIRC, it's something like a single year assuming 1g acceleration half way there and a similar deceleration after the half-way point (can't be arsed to look it up. You, dear reader, have fun with that). However, to the observer sitting on Earth, it takes much, much longer. So long that the folks sending you off will be dead, decayed, fossilized and those fossils long degraded by the time you get there. When you get back, your home planet may well not exist anymore and and thing resembling your home society will have long been lost to the sands of time. Again, no sane species is going to make such an investment of resources for what is effectively no return.

But wait, what if aliens have some magic technology which lets them bypass the limitations on the speed of light? Ok well, if little green Gandalf can cast a teleport spell on Frodo the tentacled alien, then yes he can toss his thing in whatever crack he wants. But, absent any evidence to show that such magic is possible, then it's not really worth consideration.

So, does "the government" have some secret knowledge about aliens? I highly doubt it. Mostly, because I doubt such exists. But, also consider the difficulty of maintaining such a secret for decades with possibly thousands of people knowing. One of the things you learn about, when you get a US FedGov Clearance, is the concept of "Need to Know". One of the things the US Government learned during the Vietnam War was the fact that the more people who know a secret, the more likely it is to leak. If you have a ton of time and insomnia, I highly recommend reading up on Purple Dragon. Secrets leak, all the time. Yet somehow there has been a massive conspiracy around aliens visiting Earth. Oh and that conspiracy would need to extend beyond just the US Government to include other, hostile, governments. But, the only evidence we have is blury videos and crackpots. Ya, bullshit.

So ya, ET is likely "out there", the math makes it pretty likely. At the same time, physics makes it really, really, really hard for him to get here. And no international conspiracy would be able to hide such events over decades.