Every month after the day of the conjunction of the moon (when the moon passes directly between earth and sun) brings an opportunity to look for the first appearance of the new crescent, following closely behind the setting sun in the west.
Above is a photograph I took this evening (Sunday, September 29th just after sunset) of the extremely thin new crescent moon for this month (straight up from the highest part of the tree silhouettes). The moon is following the sun down towards the western horizon. You can see by the glow on the horizon that the moon is "to the left" of the point where the sun went down, because the arc of the moon's path is coming downwards from the left side of the image, which is the southern sky as we face west in this photograph.
In other words, the path of both the sun and moon arcs across the sky for viewers in the northern hemisphere (where this photo was taken) from east to west above the southern horizon, and south in this photo is to the left, so the moon is arcing down from the left after crossing the sky above the southern horizon.
Below is another photograph showing that downward arc (the blue arrow points to the thin sliver of the new moon, and shows the angle which the moon has followed from the southern portion of the sky down into the west):
Watching for the appearance of the first sliver of the new moon after conjunction was a very serious task for the priests in many ancient cultures. You can do an online search of the texts of the biblical scriptures to see how many times the words "new moon" are mentioned. The ancient Hebrew calendar began each new lunar months with this observation, which had to be confirmed by more than one witness -- but many other ancient cultures around the world appear to have used the very same process, and in many traditional cultures this system survived up through the twentieth century.
In ancient Egypt, observing the first crescent of the new moon following conjunction was extremely important and imbued with esoteric significance. Gerald Massey (1828 - 1907), writing in Volume Two of his Ancient Egypt, the Light of the World, argues that the crescent of the new moon seen in the sky was the "bow of promise" that the world would not be again destroyed by a deluge (a deluge which Massey argues was metaphorical, and having to do with the "overthrowing of the pole" (and hence the shifting of the ages due to the motion of precession -- see Massey, Volume Two pages 550 and following).
Of this bow of promise, which he argues is seen in the new moon each month, Massey writes:
After the deluge in "the destruction of mankind" the god Ra establishes a covenant with those who have escaped from the flood. He says that what he commanded is well done, and that the destruction of his enemies removes destruction from themselves [i.e., from mankind]. "Said by the majesty of Ra, It is well done, all this. I shall now protect men on account of this. Said by Ra, I now raise my hand that I shall not destroy men," i.e., not again. The making of this covenant after the deluge is followed by the establishment of the New Year's festival under the direction of the young priestesses of Hathor. "Hence comes it that libations are made under the directions of priestesses at the festival of Hathor through all men since the days of old," (line 25). When the lunar orb has been converted into the abode of Ra by night it is said, "And there arose the crescent moon of Taht [Thoth]." Now the lnar crescent is the mythological bow (Proc. Soc. Bib. Arch,. vol vi. p. 131). The speaker in the character of the solar god issuing from the crescent moon exclaims, "I am the lion-god issuing from the bow, and therefore I shot forth" (Rit. [i.e., the Book of the Dead, which in earlier centuries was often referred to as The Ritual], ch. 132). When this was written it had been apprehended that the moon derived its light from the hidden sun, and shot the arrows forth with the growing, stretching crescent that was drawn bow-like to the full with all the force of the young lion-god. It was for this that Taht the lunar deity was wanted by Ra as his bowman by night to shoot the arrows of his light with the crescent of the monthly moon for his bow. For this the bow was set in the nocturnal heaven by Ra: "And there arose the crescent moon of Taht" = the bow. The crescent moon was figured as the bow in heaven for a sign that there should be no further deluge of destruction, because the keeping of time and season did not now depend upon the setting or non-setting stars. When time was reckoned by Tehuti the teller [Thoth], by means of the dual lunation, a power was established that no flood which had submerged the pole or drowned the heptanomis, or the heaven in ten divisions, could in future overwhelm. Thus the deluge in the stellar myths being over, and the powers of darkness being defeated and destroyed, chiefly through the direct agency of the lunar goddess Hathor, the bow of Taht was set in heaven with its promise that the wrath of Ra should not again cover the earth.
[. . .]
It has now to be shown that the bow in the Kamite mythos, which we look upon as the original [i.e., which Massey believes to be the original pattern upon which the scriptures of the Bible were later patterned], was not the rainbow, which was afterwards substituted as more natural by those who knew no better. The lunar crescent was not only the bow of the deluge and sign of promise for all future time, it was also an ark of safety from the waters of the Nun, in which the young child of light was bosomed and reborn of the lunar virgin mother. In the Osirian cult Osiris was reborn in an ark of crescent shape which was a figure of the crescent moon. It is said to Osiris in the preparatory pangs of birth, "Taht is a protection for thee. He placeth thy soul in the lunar bark in that name which is thine of god Moon" or god An, another name of Osiris (Records, vol. ii. p. 119). The ark of the new moon was a means of resurrection for Osiris on the third night after his death, if we count the 17th Athyr as one. The priests brought out the sacred coffer containing a little golden ark. They also modelled a little image of the crescent moon. 562 - 563.
Although I have found much evidence to suggest that the imagery of the deluge (found in the myths of cultures around the globe) is celestial in nature (to include the ark and the bow), this does not mean that the ancient myths do not also use lunar symbolism: the ancient system of myth imparted to humanity in extreme antiquity is amazingly sophisticated and can be shown to incorporate the movement of the sun, the planets, and the moon into its multi-layered profundity.
Thus, I have no doubt that the monthly cycle of the moon was imbued with deep esoteric meaning by the ancient system which was given to all cultures for our benefit and instruction. Massey was particularly attuned to the connection of ancient myth with the cycle of the moon (see discussion in this previous post from 2014).
The interpretation given in the passages cited above suggests that the disappearance of the moon at the period of conjunction each month, followed by the reappearance at the first sighting of the very thin new waxing crescent following the period of disappearance, was associated with the death and rebirth of the dying god (in this case, Osiris) has profound lessons for us in this very present moment.
The disappearance of the god or goddess is one of the most important patterns in myth around the world, seen in the myth of Osiris but also in other cultures in the myth of Persephone, and of Tammuz, and of Baldr, and of Rabbit Boy, and of Amaterasu, and many more. This pattern may very well illuminate aspects of our own plunge into and entanglement with the material realm during this incarnate life -- and dramatize our separation from our own essential or Higher Self, which the myths around the world show to be a nearly universal aspect of the human condition.
Our separation from our essential self is a very serious issue -- but the myths also show us that this separation is not irreversible. We can recover our connection with our own essential and authentic self, and the myths (I am convinced) point us towards the ways we can do so.
Thus, every new moon we have an opportunity to consider this vitally important subject of the recovery of our essential self.
We might even say that the ancient practice of looking intently for the first visible sliver of the new moon each month points us towards the intensity (and the regularity) with which we should be pursuing reconciliation with our own authentic self.