No, no, this world will NOT be destroyed by nuclear weapons, climate change or pandemics whether we understand it or not (not over the next 10,000 years at least).

Lord Caitanya Mahaprabhu has come to this very, very rare Kali-yuga to establish His Golden Age of the great Sankirtan Movement.

This WILL happen!

We are presently only in the very early pioneering years of the great Sankirtan Movement of Lord Caitanya Mahaprabhu (just 58 years ago did Srila Prabhupada establish ISKCON in 1966)

Lord Caitanya comes only once in a day of Brahma to one Kali-yuga out of 1000, as part of the 4 yuga's that make up a Maha-yuga that are-

Satya-yuga

Treta-yuga

Dvarpara-yuga

Kali-yuga.

All occur only between sunrise and sunset (there are no Maha-yugas during Brahma's night) 

So, both Brahma's "day-time," when the 1000 Maha-yugas happen, and Brahmas "night-time," where there are no Maha-yugas, together equals 8 billion 640 million years according to Caitanya Caritamrita CC Adi 3.10, Purport.