Aside from military conquests and ownership of land, I find that a significant factor to the success and cultural zeitgeist of certain civilizations (Greek, Roman, etc) to be Enlightenment eras.
The Ionian Enlightenment gave way to forward thinkers like <PERSON> (known for his speculation on atomic theory) and <PERSON> (who needs no introduction.) Its influence stretched into the Hellenistic period, where you had thinkers like <PERSON> and <PERSON>.
Enlightenment eras of the past are the same as modern Enlightenment eras.
But that's what they are - cultural zeitgeists. It wasn't so much individuals who just put forth their hard work and had it mooched off of (you know, like today), it was embodied in the collective conscience of the people. It pervaded society, government, and church.
You need all of society to be in on it. Values of empiricism, ethics, and culture has to be part of the collective where everyone has a shared interest. 72
To accomplish this, give your culture a religion, or some dogmatic (for lack of a better word) system where the primary cultural goal is to simply innovate on everything, and change lots of minds about large questions about our environment through that process of innovation.
For example, we hold on to the past few hundred years because minds have been changed drastically in terms of things like gravity, physics, and medicine (germ theory.)
Your government - which runs by the system or religion - would be more willing to fund projects that adhere to their belief system, in the same way King <PERSON> and Queen <PERSON> funded <PERSON> or that King <PERSON> funded <PERSON>.
You basically have to have a government that's like an oversized Royal Society - it cares not about funding as much for military conquest or funding Guantanamo Bay, but about changing minds and literature that prove to withstand the test of time.
We can't help but think about these times of innovation because everything around us only works because of the innovations made in those times. With our knowledge of thermodynamics, we have refrigeration systems. With knowledge of gravity and relativity, we have GPS.
You would think of these times with a sense of nostalgia, of charm, of simplicity, of a fount of cultural innovation, whether it's the Renaissance or the Enlightenment, because it's tied to the present. You can't be as tied to a past civilization that didn't affect you.
"If I have seen further than other men it is because I have stood on the shoulders of giants."
— <PERSON> 111