The moment the moon passes between earth and sun — which is not when anyone can see it.
Conjunction, or the astronomical new moon, is the instant the moon passes between the earth and the sun. It is calculable centuries ahead to the minute.
It is not, however, when the crescent becomes visible. At conjunction the moon is unlit from earth; the crescent appears some hours later, and how many depends on the geometry, the latitude and the clarity of the sky.
The gap between a calculable instant and an observable one is why calendars that begin months on sighting cannot simply be computed, however good the astronomy is.
Conjunction is an instant that can be computed. Sighting is an observation that may or may not succeed on the evening it is attempted.
See also moon sighting · hijri calendar · lunisolar calendar
We hold this as not stored — it is an input to the rules, not a record. See what we hold.