Nothing is impossible..... but almost everything is highly unlikely.
Because of the law of extremely big (near infinite) numbers, certain things are true:
Life exists. 100% certainty. I and you are proof.
Life exists, has existed, or will exist, somewhere else in the universe. 100% certainty, given the size of the universe and the length of time given, around 13 billion years and counting.
That we will ever be able to contact, be contacted by, or in any way encounter the other life in the universe is a 100% certainty against, given the vast distances, both in space and time involved, combined with the limiting effect of the speed of light.
One way of putting the space part of the equation into perspective is to realize the sheer number of galaxies involved. Look at the night sky, anywhere, randomly. Imagine an area the size of the moon. If you focus the Hubble telescope at that random area for a long exposure, you will see an average of 400 galaxies. Not stars, galaxies. And this is true for any point that you choose to focus on. Each of these 400 galaxies may contain an average of one hundred million stars, and a good proportion of each of those stars, in each of those galaxies, has the possibility of planets, and among those planets, there is the possibility, however small, of a planet able to sustain life "as we know it". There may be, of course, life "as we don't know it" as well. But as I stated before, the chances of encountering any of those distant life forms is effectively zero.
Sorry to be harsh, but that's just what the numbers say to me. Say, for instance, life evolves in some galaxy hundreds of millions of light years away, and advances to the point of sentience, and advances to the point of trying to communicate with other life forms, so they send out some sort of signal. It reaches us on earth! But.. life has just evolved, and the bacteria have no interest in the signal. Or, it gets here just as the sun expands to swallow the earth, in the far future, long after we're all gone. Either extreme is just as likely, that is to say, not at all, as being contacted by chance, right here and now. What I'm getting at is that I think that the odds of life at all are so infinitely small, that the odds of two sentient life systems occurring at the same time on opposite sides of the galaxy, and both getting to the same place, or one getting to the other, are so large, against, that it just isn't going to happen. The laws of time, space and probability are a harsh mistress. And this doesn't even take into account that even if we did meet a lifeform from someplace else, that we would be able to communicate with them in any way. The odds of life evolving to be mutually comprehensible multiplies another infinity by another infinity against, again. Little green or gray or whatever men? Please. Bipedalism? Please. Communication strictly through visible and auditory means only? Please. Defying the laws of physics? Double please.
Which is not to say that this should make us as a planet feel depressed or alone. Quite the opposite, in fact. We are unique, and special, and should make the most of every experience. We should not stop exploring, even though we will probably not find anything. If we did, I'd be glad, and embarrassed, but in the end, I'm not going to hold my breath. And I'm going to keep watching science fiction, but remembering that the most important word in that name is fiction.
!!!! *CORRECTION* !!!! The average galaxy contains somewhere between one hundred BILLION and one TRILLION stars. So that puts the big numbers dramatically higher! Sorry for the confusion.