I’m guessing that that’s as good as you’re going to get. There are other astronomical references in cuneiform tablets to earlier events, such as the lunar observations on the Venus Tablet of Ammisaduqa, but so far nobody has fixed them unambiguously. That is, they might refer to any one of a number of occurrences of the same type of astronomical event, separated by decades or centuries.
Other than the mere fact of an eclipse, the earliest event whose date is precisely known was a battle between the Lydians and the Medians, in Asia Minor - May 28, 585 BC. But this date is only known because the battle was interrupted by an eclipse, so perhaps it doesn’t count.
The book The Timetables of History claims the “First exactly-dated year in human history” was 4241 BCE, the year the solar calendar was first adopted in Egypt. It’s not an exact day, and I think the translation to the Gregorian calendar is based on comparative astronomical observations, but still…
As far as actual events here on Earth, rather than eclipses and such, a candidate for “earliest possible human event that can be dated to the day” is the Battle of Halys, May 28, 585 B.C.E., between the Medes and the Lydians in what is now Turkey.
Of course, the reason the Battle of Halys can be dated to the day is that traditionally the two sides called off the fighting when a total eclipse of the Sun occured (which they took as an omen); and we can date exactly when a total eclipse visible from that location would have taken place. So I guess it’s eclipses all the way down.
Oddly, there’s a complication to this case that probably strictly rules it out as even a candidate for dating something to the exact day.
When Caesar introduced what we now call the Julian Calendar there was a big screwup in the implementation. This wasn’t noticed until Augustus was emperor, forcing him to introduce a further set of reforms. Due to the patchiness of the surviving records, there’s apparently a degree of uncertainty about exactly what happened during this stage, with the result that dates in the Roman calendar prior to about 8 BCE can’t be pinned down to better than a few days. (Which is why, for instance, this converter has a disclaimer about such earlier dates.) We thus can’t say on exactly which Julian Date the Romans started 44 BCE and hence can’t exactly pin down the Ides of March that year. We thus have an exact contemporary record of the date in the Roman calendar, but can’t quite exactly match it to an absolute date.
(I didn’t realise this nuance until poking about as part of an old thread asking on which day of the week Caesar was killed. That thread seems to have gone to the Great Hamster Playground in the Sky.)