The new moon is conjunction, elongation zero, the Moon between the Earth and the Sun and therefore invisible: its lit face is turned away and it is above the horizon in daylight. This is a computed instant rather than an observation, and it is not the same thing as the first sighting of the crescent, which follows it by a day or more.
The phases are produced by the changing angle between the Sun, the Earth and the Moon, and the quantity that defines them is elongation, the Moon's angular distance from the Sun as seen from the Earth. The complete round from one new moon to the next is the synodic month, about 29.53 days, and it is longer than the sidereal month of about 27.32 days in which the Moon returns to the same place among the stars, because the Earth has moved along its orbit in the meantime and the Moon must travel further to catch up.
That distinction between the astronomical conjunction and the visible crescent divides calendars. The Hijri month traditionally begins on the sighting, so it can differ between places on the same evening; the Chinese month begins on the day of the astronomical new moon, computed rather than seen; and the Panchanga treats the moment of conjunction as the end of the thirtieth tithi, Amavasya. Three calendars, one event, three different rules for what to do with it.
A solar eclipse can only occur at new moon, and does so only when the conjunction happens near one of the two nodes where the Moon's orbit crosses the plane of the ecliptic, which is why eclipses are not monthly.
Sources AstronomyAndrew Fraknoi, David Morrison, and Sidney C. Wolff (OpenStax) with The Indian CalendarRobert Sewell and Sankara Balkrishna Dikshit, The Oxford Companion to the Year: An Exploration of Calendar Customs and Time-ReckoningBonnie Blackburn and Leofranc Holford-Strevens