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