Ah, the Fermi Paradox.
You're familiar then with the concept of the Great Filter... something that makes advanced technological life forms very rare if not effectively extinct on the galactic level. Theories abound, but mostly boil down to:
1. We're alone.
2. We're the first, or among the first.
3. We're not alone, but interstellar space travel is so hard that virtually no species manages it before their extinction.
And the Big Question is whether the Great Filter is behind us, or ahead of us, of course.
I
prefer to believe #2, of the first question, but clearly I cannot prove it. Proponents of #2 suggest that until very recently (on a stellar scale) X-ray bursts from various stellar phenomena made it improbable that advanced life would arise and survive long enough to reach our level. Also in question is whether an intelligent and technological species manages to survive long enough to achieve interstellar travel and colonize other worlds (speculation says this may be rare).
The question of a technological civilization self-destructing is an interesting one and I am skeptical. Certainly humanity is now capable of destroying
civilization as we know it, but even if we used every nuke on the planet it is improbable we'd wipe out all of humanity. Some would survive, radiation would decline over time, and civilization would eventually re-build, re-discover... and maybe start the cycle all over again.
Those familiar with Niven/Pournelle and the Mote will recognize the theme of the Cycles of rising and falling civilizations trapped in a single star system.
But even given the assumption that we wouldn't be able to wipe ourselves out utterly, the question of whether we (or another alien species) could MAINTAIN a technological civilization long enough to become a star-faring species without bombing ourselves back to the stone age is a question.
The Fermi assumptions about how a sub-light civ could populate the galaxy in a relatively short timespan also relies on a number of assumptions... namely that the species in question WANTS to do this. It's something humanity MIGHT do, but other species of sophonts might have other priorities or philosophies. Hard to say.