The new moon was just the celebration of the new month for them.
You have to connect the dots in the world of faith, because those who can are those who here by faith.
The Sun of Righteousness is figurative for God. Those who observe God's commandment are as the moon because the reflect the righteousness of God.
Jer 33:16 In those days shall Judah be saved, and Jerusalem shall dwell safely: and this is the name wherewith she shall be called,
The LORD our righteousness.
The new moon is just a slither of light, and when you see it and bare witness to this light, it is a testimony that God has appeared to man, and this was sounded out at the Feast of Trumpets as a declaration over the burnt offering.
A Hebrew text recognized that King David was as a full moon, and that was a zenith for God's light shinning on Earth
Num 10:10
Also in the day of your gladness, and in your solemn days, and in the beginnings of your months, ye shall blow with the trumpets over your burnt offerings, and over the sacrifices of your peace offerings; that they may be to you for a memorial before your God: I am the LORD your God.
What is the day of gladness?
Pro 10:28
The hope of the righteous shall be gladness: but the expectation of the wicked shall perish.
This hope is for eternal life to those who have taken hold of the Head (Christ). Taking hold of the Head is receiving instruction,with fear and trembling, and this hope is the strength to stand for those who believe the instruction.
Therefore, God's people are like the moon in that they are a reflection of God's light(commandments).