The moon is growing after the new moon day. One is not able to see the 2nd kalai of the moon as it is so thin, but can view the 3rd.' There is a great tatwartha on seeing the 3rd day waxing crescent moon. It is visible in the western sky after sunset for a brief period only. Also the sky should be clear without clouds.
Chandra is the lord of the mind. Like waxing and waning of moon mind is also having oscillations with up and down. Seeing Chandra on Chandra Darshan is similar to seeing Jothi on Sabari Mountain. Jothi swarupa God is represented by this Chandra Darshan. Lord Shiva has this crescent moon on his head.
Without seeing the 3rd phase of the moon, seeing the 4th
phase moon (the next day) is inauspicious the 4th day. Darshan of 3rd day
waxing crescent moon is very old custom and this is available in ancient Tamil
Sangam literature. Agananooru, Maduraikanji and Kurunthogai had verses on this
'Auspicious Moon Seeing' (Chandra Darshan').