Pink Diamond represents Lucifer who rebelled against the Trinity Godhead, which the Diamond Authority stands for.
Lucifer held special station over Earth as the Morning Star(Venus) before his downfall, much like how PD held dominion over Earth.
Lucifer decided that humanity did not need God to rule them. PD decided that the Diamonds needed to leave Earth alone.
Lucifer becomes the deceiver, or Devil, to convince Adam and Eve and other angels to rebel. PD becomes Rose Quartz, and convinces humans and other Gems to rebel.
War breaks out in heaven, resulting in the Devil being cast out with his demons, bound to the realm of the Earth. Rose Quartz and the Crystal Gems are left behind on earth.
PD's Earth colony was established 6,000 years ago. Biblical Chronology places the rebellion in Eden approximately 6,000 years ago(give or take from our current year)