The Pacific Rim wiki explains that the Precursors became interested in Earth during the Triassic period, or some pre-history time, but it wasn't suitable for them. Millions of years later, the pollution of humans renders Earth sustainable for the Precursors and cue invasion. But how did the Precursors know the time was right? There is no indication that they could watch the Earth, and the only hint we have that they glean any new information about Earth is the development of different Kaiju to fight the Jaegers, and the drift with the Kaiju brain. So if those are their only eyes into our world, as hinted, what told them that Earth was now ripe for colonization?
Presumably small kaiju were sent from time to time to test. The Pacific ocean is huge, and if those arrivals occurred in early history, there would be no record of it. If any accounts did survive, they'd simply be today's myths of dragons or sea monsters. There exist enough weird legends from both East Asia and the sea-faring explorations of Europeans for this to be plausible.