Skimming some material online, it looks like the best mechanism to get day-level dating for very old historical times are going to be celestial events, like eclipses, because we can run motions of those bodies backwards to compute precisely when the event occurred.
The first recorded notation referencing an eclipse dates to about 5,000 years ago, according to NASA. Spiral petroglyphs carved on three ancient stone monuments in Ireland at Loughcrew in County Meath, depict alignments of the sun, moon and horizon, and likely represent a solar eclipse that occurred Nov. 30, 3340 B.C., NASA reported.
That isn't a first (well, other than in being the first known recorded eclipse to us), but my bet is that it'll be some event on the same day or within a specified number of days of an eclipse or similar.
So that probably places an outer bound on when such an event would have been known to have occurred, unless there's some other form of celestial event recorded way, way back when.
EDIT: Though it sounds like there is some controversy as to whether that is in fact what is being depicted.
EDIT2: and also according to the article, our accuracy in running those back that far starts to fall off:
Perhaps the biggest hole in Griffin’s theory is the date of the ancient eclipse that coincided, more or less, with the tomb’s construction. Earth’s rate of rotation fluctuates just enough over time to make calculating the path of totality for prehistoric eclipses imprecise. In fact, even programs designed to make those calculations can only do so reliably about as far back as the eighth century B.C. Steele says.
“We can’t just calculate back to 3000 B.C. and say that such-and-such an eclipse was visible in a certain place,” he adds. “The 3340 B.C. eclipse might not have been visible in Ireland at all.”