https://en.wikipedia.org/wiki/Before_Present
Apparently, the "before present" time scale is commonly used in archaeology and geology, and uses an epoch date of Jan 1, 1950. And there're two reasons for this: radiocarbon dating was first standardized in the 1950s, using a reference sample from 1950; and after the 1950s, widespread nuclear testing made radiocarbon dating inaccurate.
It's actually less arbitrary and shortsighted than it seems. Future civilizations are going to face a discontinuity in the archaeological record, and it'll be roughly at the Before Present epoch date.