According to the great medieval commentator Rashi, in his very first comment on the Torah on Genesis 1:1, God could have begun the Torah with the first mitzvah, which appears in Exodus chapter 12, in Parshat Bo. (Notwithstanding that the mitzvah of Brit Milah seems to come first, in Genesis 17.)
בראשית: אמר רבי יצחק לא היה צריך להתחיל [את] התורה אלא (שמות יב ב) מהחודש הזה לכם, שהיא מצוה ראשונה שנצטוו [בה] ישראל
In the beginning: Said Rabbi Isaac: It was not necessary to begin the Torah except from “This month is to you,” (Exodus 12:2) which is the first commandment that the Israelites were commanded…
The mitzvah referred to is found in a portion that is also read yearly as Parshat Hachodesh, a stand-alone maftir every year on the shabbat preceding or coinciding with Rosh Chodesh Nissan. This parsha is understood to have been spoken by God to Moses and Aaron on Rosh Chodesh Nissan, and commands that Nissan is to be the first month of the Hebrew calendar. (After that, it continues with the command of the korban pesach – the Paschal Sacrifice – a most significant feature of the month of Nissan.)
א וַיֹּאמֶר ה אֶל-מֹשֶׁה וְאֶל-אַהֲרֹן, בְּאֶרֶץ מִצְרַיִם לֵאמֹר.
ב הַחֹדֶשׁ הַזֶּה לָכֶם, רֹאשׁ חֳדָשִׁים: רִאשׁוֹן הוּא לָכֶם, לְחָדְשֵׁי הַשָּׁנָה.
1 And the LORD spoke unto Moses and Aaron in the land of Egypt, saying:
2 ‘This month shall be unto you the beginning of months; it shall be the first month of the year to you.
While the simple meaning of this verse – the pshat – is that the year begins with the month of Nissan, in the Talmud, it is understood to mean more than that (although, not to the exclusion of the pshat.) The Talmudic Rabbis explained that this also refers to the sanctification (declaration) of the beginning of each month based on witnesses seeing the “new moon”:
גמרא מסכת ראש השנה
דף כ,א ת”ל (שמות יב) החדש הזה לכם ראש חדשים כזה ראה וקדש
Talmud – Mas. Rosh HaShanah 20a
therefore it says, ‘This month is for you the first of months’; See [the Moon] like this, and then sanctify.
דף כב,א א”ר לוי מאי טעמא דר”ש דכתיב (שמות יב) ויאמר ה’ אל משה ואל אהרן בארץ מצרים לאמר החדש הזה לכם עדות זו תהא כשרה בכם ורבנן עדות זו תהא מסורה לכם
Talmud – Mas. Rosh HaShanah 22a
Levi said: What is the reason of R. Simeon? Because it is written, and the Lord spoke unto Moses and Aaron in the land of Egypt, saying, This month shall be unto you the beginning of months, which implies, ‘this testimony shall be valid [when given] by you’. And the Rabbis? — [It implies], this testimony shall be entrusted to you.
These two quotations from Tractate Rosh Hashanah show how the rabbis explained the verse to mean that a new month begins upon (1) the seeing of the earliest sliver of the new Moon during its monthly cycle (known as the Molad; which is not exactly what scientists call a “New Moon” which is when none of it is visible) AND (2) the testifying before a court of rabbis by witnesses who saw the Moon. Then the rabbinic court declares that the new month has begun. (However, nowadays, ever since about the 4th Century CE, we have used a “fixed”, or automatic, version of this calendar, attributed to Hillel II.)

From a philosophical or theological point of view, it is understood to be of great significance that we, the Jewish people and the Jewish Courts, make the calendar based on human observations. God has given us the power and responsibility to determine the times of our (seasonal) religious observances.
The Ralbag, Rabbi Levi ben Gershon, a.k.a. Gersonides, a great medieval rabbi and astronomer (and thus obviously dear to my heart…) uses some astronomy to explain this verse. His explanation stays more focused on the pshat and understanding why Nissan is the first month:
רלב”ג על התורה
Ralbag (R. Levi ben Gershon; Gersonides): Behold, this is the month that is first of all other months, is perforce near the moment that the Sun enters at the head of the constellation ‘ram’ [Aries] or the moment that the Sun enters at the head of the constellation ‘scales’ [Libra]. For these are the two places that could possibly be the New Year from among the other Solar ‘seasons’ [equinoxes and solstices], because the circle of constellations [i.e. zodiac; the ecliptic] is divided at these points. Because the circle of the [celestial] equator divides it [the ecliptic] at them, which is not the case for the other ‘seasons’ [solstices]. And we have already learned that this month is near the moment that the Sun enters the head of the constellation ‘ram’ [Aries] because the Torah has already explained that this month is the month of Spring, inasmuch as it said “Keep the month of Spring [and make a pesach…]” (Deut. 16:1) and that in the seventh month is the harvest of the produce of the fields and vineyards completed (ibid. 16:13) and we know that would be impossible unless the first month is near the moment that the Sun enters the head of the ‘ram’ [Aries]. And that month, we know, is Nissan, as mentioned in the Mechilta.
To better understand the Ralbag’s point, let us review a bit of what we have discussed in other posts (here and here.)
Recall the model called the Celestial Sphere – in which we view the sky as a sphere around the Earth – and project the Earth’s equator onto that sphere, that is called the Celestial Equator. As the Earth travels around the Sun annually, from the point of view of people on Earth, the Sun appears to move through the Celestial Sphere along a path called the Ecliptic. The Ecliptic and the Celestial Equator intersect at two points, on the Equinoxes, and these are the times when the Sun crosses the Celestial Equator – the beginning of Spring and Autumn.

The Spring – or “Vernal” – Equinox is at a point called the “First Point of Aries”, even though it is now in the constellation Pisces.
This is because, when the ancient Hellenistic astronomer Hipparchus defined it in 130 BCE, it was located on the eastern edge of the constellation of Aries, near its border with Pisces and the star γ Arietis. This was the point at which the Sun entered the constellation Aries, hence the name First Point of Aries. Over the past 2000+ years, the Earth’s precession has caused the intersection of the Ecliptic and Celestial Equator to move along the Ecliptic and it is now in Pisces, but has retained its name as the First Point of Aries.

What Ralbag is saying is that it makes sense that the beginning of the year must occur at one of the two times when the Sun crosses the Celestial Equator – either the spring or autumn equinox. Why this must be so is not entirely obvious. Certainly, many ancient cultures did follow such reasoning, but many (e.g. Romans) did not (and so the Gregorian calendar begins in January.)
Of these, the Torah is saying that it must be the month of the spring equinox that is first and the autumn equinox is seventh. Curiously, we now have “Rosh Hashanah” the “New Year” in the fall, despite this verse and its mitzvah
As an astronomer, I must say that it’s pretty awesome that the first mitzvah is based on astronomy!
One could even say that some knowledge of astronomy is a prerequisite to this mitzvah, or at least to a thorough understanding of it. Furthermore, inasmuch as the establishment of the months of the Jewish calendar is a prerequisite to the fulfillment of many, many mitzvot, and astronomy is a necessary for that, it is also a prerequisite to all of them!
Let us again touch on the aforementioned philosophical/theological understanding of the significance of the idea that God has given us control of the Jewish calendar based on human observations. I think that it is slightly overlooked in this classic understanding, that the observations and/or calculations required of us by this mitzvah are scientific astronomical observations! Implicit in God’s giving over to us the determinations of the religious calendar is that He requires us to understand (some) science in the process!
In his essay The Lonely Man of Faith, the great modern Jewish thinker Rabbi J. B. Soloveitchik – a.k.a. The Rav – presents an explanation of the retelling of the creation of Adam and Eve in Genesis chapters 1 and 2. To summarize very briefly (and so, inevitably, to not really do the essay justice) he explains that each version presents a different aspect of humanity (Adam) in the story of creation, which he refers to as Adam 1 and Adam 2. The first Adam is created as the pinnacle of an orderly structured creation process. This Adam is the scientific, technological minded aspect of humanity, to whom God gives the mandate to “fill the earth and subdue it, and rule over the fish of the sea and over the fowl of the sky and over all the beasts that tread upon the earth.” (Genesis 1:28) The second is a human focused more on the spiritual, the arts, relationships with others – hence the detailed description of Eve’s creation because of Adam’s loneliness.
Bearing this in mind, perhaps there’s a more subtle connection between this first mitzvah and the first chapter of Genesis that/than Rashi hints at…
As Rashi said, God could have started the Torah with this mitzvah, with its implied requirement of the pursuit of science. But instead He started it all the way back with the creation of Adam, to give us the full background and a more direct reminder of our explicit divine scientific mandate.
Chodesh tov! And happy new year!