Do you really believe that in all of eternity, we happen to be just four and a half billion years in? We are probably on our infinite life, and have infinite more to go. Just completely random lives, no idea where we will end up, nothing persists.

Yes I do, though must clarify its the earth that is estimated 4.5 billion. the universe itself is currently estimated at 13.8 billion years since big bang.

There's a difference between the philosophical idea of an eternal process of cosmological rebirth, and the experimentally observed behaviors of the current universe we live in captured with our most powerful instruments and our best mathematical models.

In the 20th century we built telescopes powerful enough to see into the very distant universe and track the movement of galaxies. Because of this technological achievement we observed some strange things.

First was that galaxies seemed to be moving further and further away from each other. Not only that, they were moving away at an accelerating pace. This uncovered the idea of cosmological expansion, that over time our universe "spreads out" and creates new space between already distant objects.

Second, because the speed of light is finite, this creates fundamental limits to how far we can observe (the cosmological horizon) and a crazy cool phenomenon where the further you look into the distant universe the further back in time you look due to the age of the light from the star and the distance it traveled. We can literally see how the universe looked billions of years ago and calculate how far back we are looking.

If you look back far enough with extremely low frequency radio telescopes you can map out the thermal radiation from when the universe was extremely hot and dense about 380,000 years after the Big Bang. This is called the Cosmic Microwave Background. It shows the universe was in a very condensed high energy state.

Third, we have concepts such as the second law of thermodynamics that says entropy increases in closed systems. Energy always spreads out and systems tend toward disorder on a global level. We have equations that very accurately describe this distribution.

With these breakthroughs we had enough data to simulate accurate matter distributions of the current universe, observe and accurately model matter distributions in the distant past, and use that model to find a best prediction of what may happen in the future with what we currently know. All three lines of evidence point to a universe that is roughly 13.8 billion years old with a definite beginning and end state.

This can still be reconciled with spiritual beliefs if your willing to redefine eternity to something more like an eternal cycle of rebirth with the heat death of one universe bootstrapping the creation of the next iteration. You may enjoy Futuramas bit on it.