Odds are, after traveling all that way, if we had been visited they would have settled and we would either not exist or at a minimum we would know it.
To distinguish between "believe" and "know," I dunno -- seems to me if I believe something I also know it, even though in both cases I may be wrong. My opinion is that "they" are out there, but way, way out there -- so far that there is almost no chance of our ever detecting their presence (like maybe just one civilization in a given observable universe type rarity).
(A remark about "observable universe." Since the Big Bang, light has had a little under 14 billion years to reach us, and has been expanding all the while, so that over time more and more galaxies recede to a point where their light can never reach us -- the observable horizon -- which now consists of several hundred billion galaxies but over time as the expansion speeds up will become fewer and fewer). The real universe is, assuming inflation happened, which seems most likely, is many orders of magnitude bigger than that, if not infinite, but this is stuff beyond our ever seeing as it is receding from us (actually the space they are in is receding) faster than light, so no information about them can ever reach us.)
Of course in an infinite or at least unimaginably large universe pretty much everything that is possible will happen, and from our case we know things like us are possible. Still, there are so many points in our evolution where things could have gone wrong and are extremely unlikely, and it only takes a line of a few of these to put the odds against us into the astronomical area.
Of course we are just beginning the search, and the search is magnificently worth doing, but we should not hold our breath.
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