I know from the study of world civilizations throughout history that each comes to a final end eventually. . . .
You need to keep reading. Chinese civilization has never fallen and has been continuous for more than four thousand years. China has been conquered, first by the Mongols and later by the Communists, but in each case it absorbed and assimilated the occupiers and reemerged as China. The same can be said for India. It was conquered, first by the Mongols and later by the British, but its civilization remains intact and only a little worse for the wear. The same applies to Persia, perhaps to a lesser extent.
. . . . (as the majority have already and have faded into history) but that each is eventually replaced by a new and more advanced one.
I don't think the word "eventually" is needed. Rome was conquered by barbarians and never regained its glory, but its civilization never came to a "final end" as you put it. It did the same thing to its Germanic occupiers that China did to its Mongol occupiers: assimilated them so they wound up as heads of a relatively continuous government. And meanwhile Greece took half of that civilization and kept it going in Byzantium.
The civilization of Egypt was obliterated, but it was replaced immediately, not "eventually," by the civilization of its Muslim occupiers. The civilizations of the Aztec and the Inca were likewise obliterated (more thoroughly than Egypt: the Aztec libraries were burned), but like Egypt their civilizations were immediately supplanted by the Christian civilization of the European occupiers. Byzantium was overrun by Muslim armies, but we can hardly say it was destroyed. The glory of many of its cities is still extant.
That is what we must have very soon: a new civilization . . . one that is fitted to solve this situation.
We're living through the Paradigm Shift into the Post-Industrial Era, and the next civilization will be largely virtual. We're building it right here on the internet, and it's a perfect fit.