If you think about it, Steven said "Peridot, were you in the war?" or something like that, and peridot answered: "No, I wasn't lucky enough to be around that time. But I did read thousands of years of reports!" So obviously peridot isn't anywhere near 3,000 years old, She must be around 400 - 200 years old At least.
(Btw I got most of the information from my friend)