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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.
I searched for "first recorded eclipse":
https://www.livescience.com/59686-first-records-solar-eclipses.html
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.
https://www.atlasobscura.com/articles/oldest-eclipse-art-loughcrew-ireland
EDIT2: and also according to the article, our accuracy in running those back that far starts to fall off:
It sounds like one complexity is that while eclipses can be run accurately (maybe not where they are visible), the problem is that when the day occurred is not, and you want to know the day. Apparently, there are some unknown factors affecting the rate of Earth's rotation a bit, and the error is enough that it becomes significant across millennia.
https://theconversation.com/archeoastronomy-uses-the-rare-times-and-places-of-previous-total-solar-eclipses-to-help-us-measure-history-222709
So if you had an event that was recorded happening in conjunction with an eclipse, we could maybe tell you pretty precisely how long ago it was in units of seconds. But we wouldn't know how many days ago it was, because the day is not a fixed unit of time and we don't know sufficiently-accurately how the length of a day has changed over that period.