We know that the Citadel measures time as "years after Aegon's Conquest". Therefore, it seems reasonable to conclude they used a different system pre-Targaryen conquest, and only switched over to the system because it was a very historic occurrence. What system did the Maesters of the Citadel use before Aegon Targaryen made his realm?
We don't know... because the Maesters have not told us.
There are none who can say with certain knowledge when the world began, yet this has not stopped many maesters and learned men from seeking the answer. Is it forty thousand years old, as some hold, or perhaps a number as large as five hundred thousand—or even more? It is not written in any book that we know, for in the first age of the world, the Dawn Age, men were not lettered.
- The World of Ice and Fire, The Dawn Age
The are thousands of years of history prior to Aegon's Conquest, but the maester never really tells why they chose the conquest, just that they did.
The maesters of the Citadel who keep the histories of Westeros have used Aegon's Conquest as their touchstone for the past three hundred years. Births, deaths, battles, and other events are dated either AC (After the Conquest) or BC (Before the Conquest).
- The World of Ice and Fire, The Conquest
In addition the information may be out there, we as readers, have not been given "access"
One issue that plagues all studies of the ancient records is how differently the varied cultures reckon days and seasons and years. Archmaester Walgram's great work, The Reckoning of Time, delves deeply into this problem, but there is little consensus on what the dates we have actually mean in our own reckoning.
- The World of Ice and Fire, Other Lands
If we could get our hands on a copy of The Reckoning of Time we might have a much better answer...
For the explanation of the physical passage of those years see: What is a "year" in Westeros?
The second answer provides the most relevant information IMO.