The Age of Three Powers is very hard to obtain after a long period of time. Esspecially, to get the Age of Three Powers, you must make sure you don't have many megabeasts. If you just have a few, you make sure they earn plenty of kills and therefore become noticeable, making it 'The age of...'. On the other hand, they tend to die out after a few hundred years! Your best bet is to have very few mega beasts and stop the map creations once you reached an Age of Three Powers. This will likely be in the first few hundred years.
Having lots of beasts means they will all get some kills, but none might get enough to become noticeable and start an 'The age of...'. Also, I found it easier to get this on smaller maps. The huge distances between civilizations on large maps might make it difficult to get enough kills for the megabeasts (probably they need a % of kills, instead of a predefined number).
So, I suggest, try out having just a couple of beasts (5 mega, 5 semi, 5 colossus) and many populations with many sites. But again, I'm not sure you'll get it on a large map. And if it's really measured in % kills, you might even want to lower the amount of civilizations while keeping the sites limit up (so they don't go extinct), but as I said, it's hard on large maps. Your best bet is probably a small/smaller map.
Tell me if you found something that works!