This parsha has the unique distinction of being the organic beginning of the Torah. Rashi, in the famous opening lines to his peirush on Chumash, quotes the midrash which asks,
"shouldn't the Torah have started with the portion of 'hachodesh hazeh lochem', which is the first mitzvah that Israel was commanded? Why does the Chumash start with Bereishis? [The answer is] ...so that if the nations of the world will accuse Israel of being thieves by dint of having conquered the Land [of Israel] from the seven nations, they will reply that the entire world is G-d's; He created it and gave it to whom was fit in His eyes. He gave it to them by dint of His will, and by dint of His will took it from them and gave it to us."
This Rashi certainly can't mean that this will convince the nations of the world of anything. It hasn't for the last millennia, and by all accounts does not seem to be doing so now. Additionally, starting the Torah with hachodesh hazeh lachem seems odd. If we are meant to start the Torah with the world of mitzvos, then surely it is mattan Torah that we should start with. The Rambam (Peirush Hamishnayos) famously states that the validity of any mitzvah starts with the Sinaitic revelation. Any mitzvah given before [i.e. millah or gid hanasha] is still in effect only because it was repeated at Sinai. Why, then, would it be proper to start the Torah at our parsha?
To understand the fundamental difference between Bereishis and "hachodesh hazeh lochem", we will need to examine to fundamental contexts of "universe": natural/determined, versus "willed"/ choice. On the one hand we can posit that the most basic structure of our universe is "law and order", which fits so well with our experience of the immutable natural laws. In this context Hashem appeared and commanded particular deeds to be performed, and prohibited particular activities.
On the other hand, one may posit a supernatural context, wherein everything is the "will of G-d" and the natural order as such is but a temporary - albeit long-lived - particular "will of Hashem".
If we are to ask what is the most basic unit of our universe, we may well answer: time. It is the most unbending and unyielding of the four dimensions [Einstein aside.]
Thus Bereishis begins with time: In the beginning. The core unto of time is a day. There was night and daytime, forming "one day." This is the natural world, and time is immutable. "What was before" is irrelevant, and from the point of Bereishis on, day is a fixed unit of time. The holy day which comes out of this arrangement is Shabbos, which is characterized as "k'vi'ih v'kaymi - fixed and immutable."
But there is another unit of time called chodesh. This is an inherently fluctuating unit, as it has no direct correlation with "days"; any given month can be longer or shorter. But more importantly, its halachic status is given to change. The length of the month and its position in the year are set by humans. Humans act not only as observers of the passage of months, but we actually can add or subtract a month, as per our need.
Thus in the first model, time is fixed and man is the variable; in the second model man is fixed, i.e. atem, and time is variable.
The nations of the world have seven mitzvos, corresponding to the seven days of creation. Their world's framing context is a fixed natural order within which G-d is omnipotent. The additional miztvos that we have are not simply more of the same, but rather are a function of a different contextualization of our existence. Chazal teach us that the six hundred and thirteen miztvos represent the elements of the human body. It is the Torah of man, rather than the Torah of the world.
It would therefore not be adequate to begin the Torah at mattan Torah. We must start with redefining the universe itself, such that man is the at the core and is the central point of reference of existence, and time is his obedient servant. The corresponding alternative to Bereishis is hachodesh hazeh lochem, not the Aseres Hadibros. And, indeed, the Torah's real Genesis is hachodesh hazeh.
Hashem did not want to leave creation distributed between two frameworks, one centered on temporality and one anthropocentric, which did not interface with each other. Such a bifurcation would run counter to Hashem's unity. Translating this to the world of ethics, this would mean that a system in the universe in which Hashem was ethical according to a Torah viewpoint but seemingly unjust from the perspective of a [Divinely imbued] universal morality is unacceptable. Rather, Hashem engineered a universe in which the various articulations of His will all point in the same direction, and according to which Eretz Yisroel is understandably and justly ours from both perspectives - the perspective of hachodesh and the perspective of Bereishis.
The remarkable unity between the framework centered on time and the anthropocentric framework was not put into place to convince the nations of the world of the validity of our claim to Eretz Yisroel. Rather it was created to teach us that Torah is true both from our particularistic morality and according to its reflection in universal morality as well.
Mishpetei hashem Emmes, Tzadku Yachdav!