ואמרו לפני בראש השנה מלכיות זכרונות ושופרות מלכיות כדי שתמליכוני עליכם זכרונות כדי שיעלה זכרוניכם לפני לטובה ובמה בשופר
And recite before Me on Rosh HaShana verses that mention Kingships, Remembrances, and Shofarot: Kingships so that you will crown Me as King over you; Remembrances so that your remembrance will rise before Me for good; and with what will the remembrance rise? It will rise with the shofar.
ממאי דתשרי הוא דכתיב (תהלים פא, ד) תקעו בחדש שופר בכסה ליום חגנו איזהו חג שהחדש מתכסה בו הוי אומר זה ר"ה וכתיב (תהלים פא, ה) כי חק לישראל הוא משפט לאלקי יעקב
The Gemara raises a question: From where is it known that the day of judgment is in Tishrei? As it is written: “Blow a shofar at the New Moon, at the covered time for our Festival day” (Psalms 81:4). Which is the Festival day on which the moon is covered, i.e., hidden? You must say that this is Rosh HaShana, which is the only Festival that occurs at the beginning of a month, when the moon cannot be seen. And it is written in the next verse: “For this is a statute for Israel, a judgment of the God of Jacob” (Psalms 81:5), implying that this is the day of judgment.
זה היום תחלת מעשיך זכרון ליום ראשון
This day is the beginning of Your works, a commemoration of the first day
On the eve of Rosh Hashanah, all things revert to their primordial state. The Inner Will ascends and is retracted into the divine essence; the worlds are in a state of sleep and are sustained only by the Outer Will. The service of man on Rosh Hashanah is to rebuild the divine attribute of sovereignty and reawaken the divine desire, "I shall reign," with the sounding of the shofar. (The Kabbalistic masters)
tanya igeres hateshuvah 15
And every year there descends and radiates a new and renewed light which has never yet shone ...
For the light of every year withdraws to its source in the Essence of the Ein Sof on the eve of every Rosh HaShanah,
“when the moon is covered.” Rosh HaShanah is known as “the holiday when the new moon is covered,” and is not seen
In a spiritual context this means that the Sefirah of Malchut (represented in the Kabbalah by the moon), the light that animates the worlds and created beings, is concealed and withdraws to its source.
Afterwards, by means of the sounding of the Shofar and by means of the prayers, a new and superior light is elicited...a light of a yet higher rank to radiate to... those who dwell upon earth.
(13) And in that day, a great ram’s horn shall be sounded; and the strayed who are in the land of Assyria and the expelled who are in the land of Egypt shall come and worship the L-RD on the holy mount, in Jerusalem.
(24) This is the day that the L-RD has made— let us exult and rejoice on it.
תָּנֵי בְּשֵׁם רַבִּי אֱלִיעֶזֶר בְּעֶשְׂרִים וַחֲמִשָּׁה בֶּאֱלוּל נִבְרָא הָעוֹלָם
They taught in Rabbi Eliezer's name: On the 25th day of Elul the world was created.
"Come, let us bow down; let us bend the knee before G‑d our Maker. Zohar 3:107b
(ג) אִי הוּא חָטָא, כָּל עָלְמָא מַאי חָטְאוּ. אִי תֵּימָא דְּכָל בִּרְיָין אָתוּ וְאַכְלוּ מֵאִילָנָא דָּא, וְאִתְרְמֵי מִכֹּלָּא. לָאו הָכִי, אֶלָּא בְּשַׁעֲתָא דְּאָדָם קָאִים עַל רַגְלוֹי, חָמוּ לֵיהּ בִּרְיָין כֻּלְּהוּ, וְדַחֲלוּ מִקַּמֵּיהּ, וַהֲווּ נַטְלִין בַּתְרֵיהּ, כְּעַבְדִּין קַמֵּי מַלְכָּא. וְהוּא אָמַר לוֹן, אֲנָא וְאַתּוּן, (תהילים צ״ה:ו׳) בּוֹאוּ נִשְׁתַּחֲוְה וְנִכְרָעָה נִבְרְכָה לִפְנֵי יי' עוֹשֵׂנוּ, וְכֻלְּהוּ אָתוּ בַּתְרֵיהּ. כֵּיוָן דְּחָמוּ דְּאָדָם סָגִיד לְהַאי אֲתַר, וְאִתְדַּבָּק בֵּיהּ, כֻּלְּהוּ אִתְמְשָׁכוּ אֲבַתְרֵיהּ, וְגָרִים מוֹתָא לֵיהּ, וּלְכָל עָלְמָא.