Our Gemara on Amud Aleph contains one of the most theologically provocative aggados of all time:
What is different about the goat brought as a sin-offering of the New Moon that it is stated with regard to it: “To the Lord,” a term not written with regard to other sin-offerings? The Holy One, Blessed be He, says, as it were: This goat shall be an atonement for the fact that I diminished the size of the Moon.
In this aggadah, we find God personified, utilizing the Rosh Chodesh sin-offering to obtain forgiveness for Himself, in that He reduced the light of the moon. Obviously, we cannot take this teaching at face value. God cannot sin because He cannot be anything other than perfect and wise. If God were subject to any mistake, no matter how small, that would be an imperfection and indicate physicality and limits, which is an affront to His unity and omnipotence.
The Tiferes Yosef (Likkutim Pesach 6) explains this in depth, and I will attempt to summarize and convey the philosophical and theological principles behind it.
What is sin? From a human perspective, we may define it as a moral violation or deficiency, but looking at it from a godly perspective, it is simply doing things that push away or distance from God’s will and presence. A mitzvah is God’s will, and a sin is acting against His will, leaving us in the world subject to the consequences of disconnection from God.
If so, what can a “Godly” sin be? Based on this definition, we might say that it has nothing to do with a moral failing, but it does have to do with something that pushes the world further away from God.
The key idea behind the monthly waxing and waning of the Moon is that, in a certain sense, it is an illusion created by the perception of the human vantage point. That is, the moon is always “full”; it just appears to grow and shrink depending on how much of the sun’s light reaches the moon and how much is blocked by the earth. At the moment of the molad, the new moon is utterly invisible because the earth is completely blocking the light of the Sun from reaching it; then we begin to see a sliver as some light reaches the Moon. The point is that none of it is real. It is only human perception. So too, when God created the world, He had to make space for physicality and withdraw, and we humans, especially Jews following the revelations of the Torah, must independently bring the physical back to God. We could only become physical because He withdrew to allow for us. But then, it is only in our physical state that we can independently bring ourselves back toward God. This is symbolized in the moon’s disappearing and then reappearing. Nothing changes with the Sun, and nothing changes with God. However, our vantage point must change in order to receive connection with God as the earth shifts to allow us to perceive illumination of the moon from the sun.
The sacrifice on Rosh Chodesh represents this original sin of sorts, the recognition that the perceived reality from the vantage point of man, who initially loses his connection to God in his own physical creation and coming into existence, is, in the allegory, God’s “sin” of shrinking the moon’s light. Man’s seeking God out is the final step, closing the loop and bringing the physical back to the godly, represented by the full illumination of the moon.
Translations Courtesy of Sefaria, except when, sometimes, I disagree with the translation 
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Rabbi Simcha Feuerman, Rabbi Simcha Feuerman, LCSW-R, DHL is a psychotherapist who works with high conflict couples and families. He can be reached via email at simchafeuerman@gmail.com