Now given that we are in the very, very, very, extremely early beginning of that period, I don't quite see the rational for the debate about whether it began at the advent of the industrial age or maybe the first 'Out of Africa' migration or perhaps August 6, 1945. The assumed fact is that somewhere far in the future, we're talking tens of millions of years; but somewhere out there, a species, probably not us, will be able to discern, imply and/or speculate about our time on this planet by looking at the geological record probably in rock that now lies as accumulating sediment on the ocean floor.
I suppose this discovery could be made by our own progeny, assuming the next extinction event is not 100% lethal. Then factoring in a dark age following the ELE and the old "history becomes legend, legend becomes myth" mists of time; then perhaps our far distant ancestors might be trying to figure us out by looking at the rocks of the future.
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Graphic Representations of the Anthropocene Age
Did we really do that tomorrow?