I completed the Colossus in 175 and continued peaceful expansion. Shaka declared on Sitting Bull in 580 and captured one city that had been settled on his island. (After their war ended in 1200, he and Pacal would occasionally start plotting, but they'd never again declare war. Seems like they didn't know how to mount naval invasions.)
I, on the other hand...
Declared on Joao in 920. He was willing to capitulate after I took two cities, but I pressed on to capture Lisbon, then accepted his capitulation in 1140.
In 1160, I attacked Sitting Bull, who was technically still at war with Shaka. They made peace, then I let SB bend the knee in 1230, after taking two of his cities.
Shaka was my largest opponent. Although my units were superior, I didn't feel that I had enough of them, yet. (Lack of hammers seemed to be a problem everywhere, in this game.) So my fleet doubled back and attacked Isabella in 1360. I accepted her capitulation in 1440, after taking four cities, including Madrid.
As I moved the fleet again to take on Shaka, I researched Military Science and finally traded for Astronomy. That was useful for the galleons and frigates, although it cost a lot to make the Colossus obsolete. With production still in short supply, I found it worthwhile to build/whip berserkers and then pay to upgrade them to grenadiers. I declared on Shaka in 1535. He was stubborn; I had to capture ten cities and raze one more before he bent the knee in 1630, with only three cities left.
The Mayan War went much easier, only lasting from 1640 to 1655, when Pacal joined my collection of vassals. Then I attacked Mansa Musa in 1660, whose capitulation gave me a conquest victory in 1690.