It looks like jews kept track of the priestly divisions after the destruction of the Temple.
en.wikipedia.org
Following the Temple's destruction at the end of the First Jewish Revolt and the displacement to the Galilee of the bulk of the remaining Jewish population in Judea at the end of the Bar Kochva Revolt, Jewish tradition in the Talmud and poems from the period record that
the descendants of each priestly watch established a separate residential seat in towns and villages of the Galilee, and maintained this residential pattern for at least several centuries in anticipation of the reconstruction of the Temple and reinstitution of the cycle of priestly courses. Specifically, this Kohanic settlement region stretched from the Beit Netofa Valley, through the Nazareth region to Arbel and the vicinity of Tiberias. In subsequent years, there was a custom of publicly recalling every Sabbath in the synagogues the courses of the priests, a practice that reinforced the prestige of the priests' lineage.[8] Such mention evoked the hope of return to Jerusalem and reconstruction of the Temple.
A manuscript discovered in the Cairo Geniza, dated 1034 CE, records
a customary formula recited weekly in the synagogues, during the Sabbath day: "Today is the holy Sabbath, the holy Sabbath unto the Lord; this day, which is the course? [Appropriate name] is the course. May the Merciful One return the course to its place soon, in our days. Amen."[9] After which, they would recount the number of years that have passed since the destruction of Jerusalem, and conclude with the words: "May the Merciful One build his house and sanctuary, and let them say Amen."
Luke 1 5In the time of Herod king of Judea there was a priest named Zechariah, who belonged to the priestly division of Abijah,
Since there were 24 priestly divisions where each served from sabbath to sabbath... it's just a matter of counting (n x 24 weeks) backwards to track the
the priestly division of Abijah.
As can be seen from this priestly divisions wiki
link...the sacerdotal courses are still tracked. And the most recent course of Abijah began on sabbath 14/5/2022... and then of course ended one week later on sabbath 21/5/2022.
So if the
the priestly division of Abijah began on sabbath 14/5/2022 then it also began every (n x 24 weeks) earlier... and so Zechariah the father of John the Baptist began his priestly course in the Temple where he met the angel Gabriel... on one of those dates below.
Counting backwards (4397 x 24 weeks) from sabbath 14/5/2022 comes to sabbath 22/11/2 BC.
Counting backwards (4398 x 24 weeks) from sabbath 14/5/2022 comes to sabbath 7/6/2 BC.
Counting backwards (4399 x 24 weeks) from sabbath 14/5/2022 comes to sabbath 21/12/3 BC.
Counting backwards (4400 x 24 weeks) from sabbath 14/5/2022 comes to sabbath 6/7/3 BC.
Counting backwards (4401 x 24 weeks) from sabbath 14/5/2022 comes to sabbath 19/1/3 BC.
Counting backwards (4402 x 24 weeks) from sabbath 14/5/2022 comes to sabbath 4/8/4 BC.
Counting backwards (4403 x 24 weeks) from sabbath 14/5/2022 comes to sabbath 17/2/4 BC.