“This day is the beginning of Your works, a remembrance of the first day.”1זֶה הַיּוֹם תְּחִלַּת מַעֲשֶׂיךָ זִכָּרוֹן לְיוֹם רִאשׁוֹן,
The Tzemach Tzedek, [whose birthday is celebrated the day before Rosh HaShanah,]2 questions:3וּמְדַיֵּק אַדְמוֹ"ר הַצֶּמַח-צֶדֶק [בַּעַל יוֹם הַהֻלֶּדֶת דְּעֶרֶב רֹאשׁ הַשָּׁנָה],
On the surface, there is a contradiction between the beginning of the quote and its conclusion.דְּלִכְאוֹרָה יֵשׁ כָּאן סְתִירָה מֵרֵישָׁא לְסֵיפָא,
The meaning of the phrase “This day is the beginning of Your works,” (i.e., the actual beginning,) isדְּפֵרוּשׁ זֶה הַיּוֹם תְּחִלַּת מַעֲשֶׂיךָ (תְּחִלָּה מַמָּשׁ) הוּא
that Rosh HaShanah (“This day”) is the beginning of all existence, the day when all the worlds first come into being, i.e., all worlds are now being created anew.שֶׁבְּרֹאשׁ הַשָּׁנָה (זֶה הַיּוֹם) הוּא הַתְחָלַת הִתְהַוּוּת כָּל הָעוֹלָמוֹת,
The intent is that on every Rosh HaShanah, all the worlds come into existence anew,הַיְנוּ שֶׁבְּכָל רֹאשׁ הַשָּׁנָה מִתְהַוִּים כָּל הָעוֹלָמוֹת מֵחָדָשׁ
All existence must be renewed each year. The life-energy drawn down every Rosh HaShanah (including the first Rosh HaShanah at the beginning of Creation) is only for one year.4 On the eve of every Rosh HaShanah thereafter, the life-energy for all existence reverts to its initial state5 and must be drawn down anew through the Jews’ prayers and their sounding of the shofar.
just as they came into existence from absolute nothingness on the very first Rosh HaShanah of Creation.כְּמוֹ שֶׁהָיָה בַּפַּעַם הָרִאשׁוֹנָה,
By contrast, the meaning of the conclusion of this phrase, “a remembrance of the first day,” is that every year, Rosh HaShanah merely commemorates “the first day,” the first Rosh HaShanah.וּפֵרוּשׁ זִכָּרוֹן לְיוֹם רִאשׁוֹן הוּא שֶׁרֹאשׁ הַשָּׁנָה הוּא רַק זִכָּרוֹן לְיוֹם רִאשׁוֹן.
The Tzemach Tzedek proceeds to explain thatוּמְבָאֵר בָּזֶה,
two elements are manifest in our commemoration of Rosh HaShanah.דִּבְְרֹאשׁ הַשָּׁנָה יֶשְׁנָם שְׁנֵי הָעִנְיָנִים,
It is “the beginning of Your works” and it is also “a remembrance of the first day.”שֶׁהוּא תְּחִלַּת מַעֲשֶׂיךָ וְשֶׁהוּא זִכָּרוֹן לְיוֹם רִאשׁוֹן.
From the fact that first it is stated that Rosh HaShanah is “the beginning of Your works,” and only afterwards do we add that it is “a remembrance of the first day,”וּמִזֶּה שֶׁבִּתְחִלָּה אוֹמְרִים שֶׁרֹאשׁ הַשָּׁנָה הוּא תְּחִלַּת מַעֲשֶׂיךָ וְאַחַר כָּךְ מוֹסִיפִים שֶׁהוּא זִכָּרוֹן לְיוֹם רִאשׁוֹן,
it is evident that Rosh HaShanah’s being “a remembrance of the first day” reflects a loftier dimension of the day6 than the fact that it is “the beginning of Your works,” for spiritual matters are characterized by a pattern of continuous ascent.מוּכָח, דְּזֶה שֶׁרֹאשׁ הַשָּׁנָה הוּא זִכָּרוֹן לְיוֹם רִאשׁוֹן הוּא נַעֲלֶה יוֹתֵר מִזֶּה שֶׁהוּא תְּחִלַּת מַעֲשֶׂיךָ.

Summary

Seemingly, the phrase, “This day is the beginning of Your works, a remembrance of the first day,” reflects an inherent contradiction. On one hand, “This day is the beginning of Your works” implies that Rosh HaShanah (“This day”) is the beginning of all existence; it is not merely the anniversary of Creation. It is the day when all the worlds come into being (“come into being” in present tense). Every year, creation is renewed. By contrast, the phrase “a remembrance of the first day” indicates that Rosh HaShanah merely commemorates “the first day.”
In resolution: Rosh HaShanah contains both elements, each one highlighting a different dimension of the day. Since spiritual matters are characterized by a pattern of continuous ascent, the fact that the description of Rosh HaShanah as “a remembrance of the first day” is stated as the concluding phrase demonstrates that this is a loftier dimension of the day than the fact that it is “the beginning of Your works.”