From the linked question:
The Original Series, the Star Trek Guide:
Pick any combination of four numbers plus a percentage point, use it
as your story's stardate. For example, 1313.5 is twelve o'clock noon
of one day and 1314.5 would be noon of the next day.
From the Star Trek: The Next Generation Writer's/Director's Guide:
A stardate is a five-digit number followed by a decimal point and one
more digit. Example: "41254.7." The first two digits of the stardate
are always "41." The 4 stands for 24th century, the 1 indicates first
season. The additional three leading digits will progress unevenly
during the course of the season from 000 to 999. The digit following
the decimal point is generally regarded as a day counter.
And from the Stardate page on Memory Alpha that the other answer references, evidence that TNG/DS9/VOY-era used decimal digits the same as TOS-era:
In addition to the overall rate of approximately 1,000 units per year,
many episodes confirm the 24-hour stardate unit which was first
mentioned in the TOS bible, with midnight at .0 and noon at .5.
So, how did I come up with that particular date?
In-universe, the first season of TNG occured in 2364. Stardate 64333.4 is (64-41=23) 23 years after Stardate 41xxx, the first season of TNG. So 64xxx corresponds to the year 2387 (2364+23).
It is 1/3rd through the year because 333 is about 1/3rd of 1000, the length of a year.
9:30 AM comes from the .4, which means the day is 40% completed. According to Google, that's 9.6 hours - 9:36 AM.