Right. I doubt that climate change alone could lead to human extinction. But climate change could bring starvation, chaos and war. And there are tens of thousands of nuclear weapons.
But yes, probably not extinction.
More likely is collapse of industrial civilization. That will cut CO2 emissions, and climate will recover is a few centuries. Many other species will go extinct in the process, however. It'll be a major extinction event.
Why?
It doesn't look like we are staring extinction right in the face.
Any talk of reasonable influence on climate is over a few centuries.
So why do do you its 'late'?