I laughed at the religious leader/no universal religion bit.
Something these threads don't consider is if the aliens land somewhere else they could end up encountering a different calendar depending on who they talk to. In Japan the era changes with the reigning emperor, so while they follow Gregorian for International Business and Holidays, locally when the Emperor came to power is still often referenced for the purposes of counting years.
Here's a primer: https://homepages.cwi.nl/~aeb/go/misc/jdate.html
This is my favorite JavaDoc https://docs.oracle.com/en/java/javase/17/docs/api/java.base...
Btw. - and maybe this is mentioned somewhere in the twitter thread - the reason we add the extra day to February is because that used to be the last month of the year, hence months september, october, november, december having names that reference 7, 8, 9, 10.
https://twitter.com/foone/status/1572260363764400129