Earth has been around for 4.5 million years. Humans have only been around for 300,000 years approximately. With only a few hundred years of the industrial age.

Would a few hundred years really cause an extinction event?

That's interesting to think about..... Perhaps it'll take a few hundreds/thousand years to fix. If it can be fixed.... Or we get hit by an asteroid first.....

Between cutting down all of the trees and other pollutants, like these so called environmentalists flying around in their own private jets, it'll be fun for a while.

Either the humans will die off due to global warming/runaway greenhouse effect before interstellar travel is achieved, or the humans will die off due to the suns transformation into a red giant before interstellar travel is achieved.

IDK. Either way, we won't be here for long. But the earth will be long after us.

Will technology save the human race beyond the two inevitable events? Probably not.