To explain the concept (why Rosh HaShanah, the anniversary of man’s creation, is considered “the beginning of Your works”) on a deeper level:וּבֵאוּר הָעִנְיָן (שֶׁרֹאשׁ הַשָּׁנָה, יוֹם בְּרֹא אָדָם הָרִאשׁוֹן, הוּא תְּחִלַּת מַעֲשֶׂיךָ) בְּעֹמֶק יוֹתֵר,
The maamar proceeds to offer a deeper resolution of the question how Rosh HaShanah can be considered “the beginning of Your works,” when in fact, the world was created beforehand. The fundamental thrust of the explanation is that not only did the creation of man generate the potential for a new and higher revelation of G‑dliness in the world, but it also elevated the existence of everything created beforehand. Thus, it serves as a beginning not only for man, but for all of creation. Rosh HaShanah is therefore commemorated as the anniversary of all creation, not only the creation of man.
It is well known that man’s Divine service has the power to change the past.הִנֵּה יָדוּעַ שֶׁעֲבוֹדַת הָאָדָם בְּכֹחָהּ לְשַׁנּוֹת גַּם אֶת הֶעָבָר.
Not only can a person change his own past, as reflected in the Divine service of a baal teshuvah, about whom it is said:1 “When a person’s repentance is motivated by love, his sin is eradicated as if it never existed,” he also has the potential to change the past of entities aside from his own self. This is what is important in this context, for as the maamar proceeds to state, the focus is on how the Divine service of Adam, the first man, affected the past of the entire world. Thus, our Sages rule2 that [when] a sage nullifies a vow, [it is considered] as if the vow was never made. To clarify the implication of that ruling, our Sages distinguish between the following two instances:
a) A man consecrated a woman on the condition that she does not have physical blemishes. She did, but she later went to a doctor who surgically removed them.
b) A man consecrated a woman on the condition that she was not bound by vows. She was, but she later went to a sage who nullified them.
In the first instance, the consecration is not effective. Even though the doctor healed the woman and she is presently free of blemishes, she did have blemishes at the time she was consecrated. Hence, her consecration is invalidated. In the second instance, the consecration is effective. Even though she had taken vows (which were nullified only at a later date), the sage’s nullification causes it to be considered as if she never made the vow. This reflects how a person can have an effect not only on one’s own past, but also on the past of people and situations other than himself.
Similarly, the Talmud Yerushalmi3 rules that the court’s decision to ordain a leap year retroactively affects a woman’s physical status.
It is understood that the above (most certainly) applies to the Divine service of Adam, the first man,וּמִזֶּה מוּבָן (בְּמִכָּל שֶׁכֵּן) בְּנוֹגֵעַ לַעֲבוֹדָתוֹ שֶׁל אָדָם הָרִאשׁוֹן
who was “the handiwork of the Holy One, blessed be He,”4 and certainly had superlative spiritual potential.שֶׁהָיָה יְצִיר כַּפָּיו שֶׁל הקב"ה,
The spiritual ascent that he brought about within all the created beings through declaring “Come let us prostrate ourselves… before G‑d Who made us,” also had an effect on their existence before he carried out his service.שֶׁהָעִלּוּי שֶׁפָּעַל בְּכָל הַנִּבְרָאִים עַל יְדֵי הַכְרָזָתוֹ בֹּאוּ נִשְׁתַּחֲוֶה גו' לִפְנֵי ה' עֹשֵׂנוּ הוּא גַם בְּנוֹגֵעַ לִמְצִיאוּתָם שֶׁלִּפְנֵי עֲבוֹדָתוֹ.
For from the very outset, the intent of the Creation was that man, through his Divine service, would draw down the revelation of G‑dliness into the world.5דְּכֵיוָן שֶׁכַּוָּנַת הַבְּרִיאָה מִלְּכַתְּחִלָּה הִיא שֶׁהָאָדָם עַל יְדֵי עֲבוֹדָתוֹ יַמְשִׁיךְ גִּלּוּי אֱלֹקוּת בָּעוֹלָם,
To cite a parallel: Our Rabbis speak6 of an instance when a man consecrates a woman on the condition that a certain stipulation is fulfilled and he uses the wording al menas (“on the condition”) when stating that stipulation. When that stipulation is fulfilled, the consecration is effective not only from the time the stipulation was fulfilled, but retroactively, from the time of the actual consecration, when the stipulation was stated. Similarly, the world was created so that man would elevate it and infuse G‑dliness into it. This was, as it were, the condition of its very creation.
Accordingly, after G‑dliness was drawn down into the world through man’s Divine service, the nature of the world’s prior existence was also elevated.לָכֵן, לְאַחֲרֵי שֶׁנִּמְשַׁךְ בָּעוֹלָם גִּלּוּי אֱלֹקוּת נַעֲשָׂה עַל יְדֵי זֶה עִלּוּי גַּם בִּמְצִיאוּת הָעוֹלָם שֶׁהָיָה לִפְנֵי זֶה,
This applies, in particular, since the world was brought into being in a manner that prepared it for the revelation of G‑dliness that man would draw down through his Divine service. For the world was created to be G‑d’s dwelling.7וּבִפְרָט שֶׁעִנְיָנוֹ הוּא הֲכָנָה לְהַגִּלּוּי שֶׁנִּמְשָׁךְ עַל יְדֵי עֲבוֹדַת הָאָדָם.
Despite the fact that the world was created on the 25th of Elul, Rosh HaShanah can be termed “the beginning of Your deeds,” for it was only then that the possibility for the fulfillment of the purpose of Creation began. True, this was the intent of the creation of the world from the outset and thus, it could be argued, that man’s creation did not introduce a radically new element into existence. This, however, is not so. Since the prevailing spiritual state of the world is one of Divine concealment – indeed, this is reflected in the very name of the world, olam, which relates to the term helem, “concealment”8 – the world’s purpose (that its existence before man’s Divine service is for the sake of, and thus in preparation for, the revelation to be brought about by that service) is also concealed. Moreover, it is not possible that there be a revelation of G‑dliness in the world as the world exists in and of itself (before man’s Divine service and certainly, before man’s creation). Thus, the revelation of the true purpose of the world’s prior existence that was brought about on Rosh HaShanah was a new development, the beginning of a radical new phase of existence that was not possible beforehand.
On one hand, to emphasize the connection between Rosh HaShanah and the entire creation, the maamar explained that, from the outset, the world was created with the intent that man reveal its G‑dly nature. Nevertheless, to highlight why this process of revelation is particularly associated with Rosh HaShanah – and thus why it, and not the 25th of Elul, is celebrated as the anniversary of Creation – the maamar explained that not only was this intent hidden, but it was not possible for it to be realized until man’s creation.
This is what is meant by the statement that Rosh HaShanah, the day of man’s creation, is “the beginning of Your works,” the fulfillment of Creation.וְזֶהוּ מַה שֶּׁהַיּוֹם דְּרֹאשׁ הַשָּׁנָה, יוֹם בְּרֹא אָדָם הָרִאשׁוֹן, הוּא תְּחִלַּת מַעֲשֶׂיךָ,
The simple meaning (and the true meaning, for the true meaning of any verse never entirely departs from its simple meaning) ofדְּפֵרוּשׁ הַפָּשׁוּט (וְאֵין עִנְיָן יוֹצֵא מִידֵי פְשׁוּטוֹ)
the term “the beginning of Your works” is the beginning of all works,דִּתְחִלַּת מַעֲשֶׂיךָ הוּא הַתְחָלַת כָּל הַמַּעֲשִׂים,
including even the works of the first five days of Creation, before man was created,גַּם הַמַּעֲשִׂים שֶׁהָיוּ בְּה' יָמִים הָרִאשׁוֹנִים דְּמַעֲשֵׂה בְרֵאשִׁית
(which also includes even the dimension of time that comprised these days)9(כּוֹלֵל גַּם הַזְּמַן דְּיָמִים אֵלּוּ),
since through the Divine service of Adam, the first man, the very being of the world that existed beforehand was elevated, and this elevation represented a radically new dimension of its existence.כִּי עַל יְדֵי עֲבוֹדָתוֹ שֶׁל אָדָם הָרִאשׁוֹן נַעֲשָׂה עִלּוּי וְחִדּוּשׁ גַּם בְּהַמְּצִיאוּת דְּעוֹלָם שֶׁהָיָה לִפְנֵי זֶה,
Therefore, this day is “the beginning of Your works,”וְלָכֵן זֶה הַיּוֹם הוּא תְּחִלַּת מַעֲשֶׂיךָ,
the beginning of the entire Creation.הַהַתְחָלָה שֶׁל כָּל הַבְּרִיאָה.
And on the very first Rosh HaShanah, the day of man’s creation enabledוּכְמוֹ שֶׁבְּרֹאשׁ הַשָּׁנָה בַּפַּעַם הָרִאשׁוֹנה, בְּיוֹם בְּרֹא אָדָם הָרִאשׁוֹן,
fulfillment to be realized within the Creation (“Your works”).נַעֲשָׂה שְׁלֵמוּת הַבְּרִיאָה (מַעֲשֶׂיךָ),
This was a radical and new development,וּבְאֹפֶן שֶׁל חִדּוּשׁ
(and therefore, it is termed “the beginning of Your works”).(תְּחִלַּת מַעֲשֶׂיךָ),
Similarly, each year on Rosh HaShanah,עַל דֶּרֶךְ זֶה הוּא בְּרֹאשׁ הַשָּׁנָה שֶׁבְּכָל שָׁנָה וְשָׁנָה,
through the Jews’ coronation of G‑d as their King and King of the entire world,דְּעַל יְדֵי שֶׁיִּשְׂרָאֵל מַכְתִּירִים אֶת הקב"ה שֶׁיִּהְיֶה מֶלֶךְ עֲלֵיהֶם וְעַל כָּל הָעוֹלָם,
the entire Creation is renewed and brought to a heightened state of fulfillment.נַעֲשָׂה שְׁלֵמוּת וְחִדּוּשׁ בְּכָל הַבְּרִיאָה,
Moreover, as a result, fulfillment and renewal is also generated in the spiritual realms above.וְעַד שֶׁעַל יְדֵי זֶה נַעֲשָׂה שְׁלֵמוּת וְחִדּוּשׁ גַּם לְמַעְלָה,
As the Maggid of Mezritch10 and the Alter Rebbe11 interpreted the teaching of the mishnah:12 “Know what is above you”:כְּתוֹרַת הָרַב הַמַּגִּיד וְאַדְמוֹ"ר הַזָּקֵן עַל מַאֲמַר הַמִּשְׁנָה דַּע מַה לְּמַעְלָה מִמָּךְ,
That everything in the spiritual realms above is from you, i.e., dependent on man’s Divine service.דְּכָל הָעִנְיָנִים שֶׁלְּמַעְלָה הֵם מִמָּךְ.

Summary

This section presents a deeper resolution of the question of how Rosh HaShanah can be considered “the beginning of Your works,” when in fact, the world had already been created. Not only did the creation of man generate the potential for a new and higher revelation of G‑dliness in the world, it retroactively elevated the existence of everything created beforehand. Since the world was created so that man would elevate it and infuse G‑dliness into it, when G‑dliness was drawn down into the world, the nature of the world’s prior existence was also elevated. Therefore, Rosh HaShanah is commemorated as the anniversary of all creation, not only the creation of man. Each year, on Rosh HaShanah, through the Jews’ coronation of G‑d as their King and King of the entire world, the entire Creation is renewed and brought to a heightened state of fulfillment.