Imbarkus
As Sartre noted in his contemplation on Hell in No Exit, the true horror is other members.
The galaxy is massive, but there are a ton of planets in it, maybe it's filled and teeming with life and the only reason we haven't noticed any is because we've been lucky. The chance might be small that they stumble upon us, which is why I think the destruction-hypothesis is more likely to happen as we do broadcast our existence into every direction.
We are isolated by both space and time. How long have we been intelligent enough for us to contact aline life? 50 years? And what are the odds we will still be here in another 1,000 years, intelligent, ready and available to be contacted or conquered?
With our Solar System's lifespan of 4 billion years, we are already a needle in a haystack to run across, even if alien life has been regularly tromping around our solar system.
This is our isolation within time, without even bringing up relativity and its impact on our isolation within space.
We will not be meeting any alien species, guys. They probably lived and died millennia before us, or will millennia after. What are the odds our worlds would develop civilizations at roughly the same time frame?