We know that all life tries to reproduce and spread, from the tiniest virus to the largest whale. It seems unlikely that any alien life wouldn't have the same impulses - because if they didn't, they wouldn't be successful as a lifeform -- same as on earth, natural selection would prevail.
If intelligent life does manage to develop to a point where self-sustaining and replicating space ships can be built without wiping itself out (which for humans should be within 500 years of doing assuming no technology regressions), then within another 200 years they'll have started to colonized neighboring star systems, and in 400 years will have reached to at least 20 light years
If we can survive to a self-sustaining colony on Mars and in asteroid belts, there are few events that would wipe out the species. If the technology is there, the growth is exponential. Certainly once we go interstellar, we should avoid any extinction level event that we know of, even Earth's star going supernova (which it can't) wouldn't be enough.
Without warp drive (or some form of FTL travel), Interstellar wars can't happen, because of the distance and energy/resource use. There's simply no point even if it were possible, but because expansion would be exponential to wherever there is matter and energy, even if attacks were launched from Earth, they wouldn't reach the outer colonies before those had further "reproduced".
Assuming no regression (major wars, cultural problems, supervolcanos, major asteroid impacts etc), but also assuming no massive leaps in technology like warp drive), by 4000AD humans will be occpuying several thousand star systems. In 10,000 light years we'll have spread at least 1000 ly in all directions. In a million years we'll have occupied the entire galaxy. This wouldn't be a single civilisation though, communication out of the solar system with human lifetimes is simply too slow.
Any group capable of intersteller travel is capable of destroying earth (the latter is far easier than the former - it's probably within the reach of some individuals now, let alone governments), so they aren't keeping away from us because we might fire a missile at them.
That there are no spacefaring civilizations mining our asteroid belt suggests that
1) In the period from 13,000 million years ago to about 1 million years ago, no life has managed to evolve far enough to reach self-sustaining spaceflight in our galaxy
2) Life has evolved to that point in the last million years, and just hasn't reached us yet
3) FTL travel is possible, there is a single civilisation that has determined our solar system to be off limits, and manages to enforce that.
(1) is 13,000 times more likely than (2), so we can ignore (2).
(I'm not including life evolving into inactivce ascended beings because there's no real framework to base that on, it would be similar to life not wanting to replicate -- why would all lifeforms evolve in that way? What evolutionary advantage does it have? Even if 99% of life did, the remaining life would quickly expand to fill the void. I'm not including life evolving into active ascended beings either because that's just saying god did it. )
Personally I'd hope for (3), but that still seems massively unlikely, because it still leaves us with the time issue - in Trek pretty much all species, from the Dominion and Borg to the Mintakens and the Hill People, are within a couple thousand years of human development. To have a civilisation that's stable enough across millions of years seems unlikely.
You can try to explain this by the progenitors seeding the galaxy with life at the same time, but that was 4.5 billion years ago. The Klingon homeworld evolving just 0.1% faster than Earth would put Klingons occupying the entire galaxy 3 million years before homo sapiens were a thing.
I have high hopes that we'll get self-sustaining space colonies (Moon, Mars, asteroids, Venus) in the next 40 years. For the first time since the 60s I think there's an outward facing optimism that space can be tackled.
