Encounter is a pretty vague term. Do I think we'll have meaningful conversation with Aliens any time in the next thousand years? Probably not. Hubble can see billions of light years out at this point meaning if something was within a couple hundred light years of us we'd probably know about it.

There could be societies far more advanced than ours since our sun didn't show up for about 10 billion years into the Universe's life. Those societies may be able to travel faster than light. But even if that is true they'd need to find us and I consider that unlikely. Because while traveling faster than light may be possible it doesn't change the facts that (a) the universe is huge and (b) light still only travels at light speed so you can't see things in real time. So even if they could get to us they wouldn't know where to look.

What's interesting to me is we might get to see the beginnings of one of these civilizations. Since we're basically looking billions of years into their past we might see another civilization long before we can do anything about it.