\ (כז) שׁוֹר אוֹ כֶשֶׂב אוֹ עֵז כִּי יִוָּלֵד וְהָיָה שִׁבְעַת יָמִים תַּחַת אִמּוֹ וּמִיּוֹם הַשְּׁמִינִי וָהָלְאָה יֵרָצֶה לְקָרְבַּן אִשֶּׁה לַיהוָה.
(27) When a bullock, or a sheep, or a goat, is brought forth, then it shall be seven days under the dam; but from the eighth day and thenceforth it may be accepted for an offering made by fire unto the LORD.
7 represents the natural world, the world was created in 7 days, 7 musical notes, 7 colors in the rainbow. Shabbos is the seventh day of the week.
(ג) שֵׁשֶׁת יָמִים תֵּעָשֶׂה מְלָאכָה וּבַיּוֹם הַשְּׁבִיעִי שַׁבַּת שַׁבָּתוֹן מִקְרָא קֹדֶשׁ כָּל מְלָאכָה לֹא תַעֲשׂוּ שַׁבָּת הִוא לַיהוָה בְּכֹל מוֹשְׁבֹתֵיכֶם.
(3) Six days shall work be done; but on the seventh day is a sabbath of solemn rest, a holy convocation; ye shall do no manner of work; it is a sabbath unto the LORD in all your dwellings.
Sources 1-4 are from the reading for Sukkoht from the Torah. The holidays are presented in chronological order from creation.Shabbos (7 Days) starting from creation. Then the creation of the Jews during Yitziyat Mitzrayim (Paysach) to Matan Torah (Shavuot) is seven weeks. Then Seven months from Yitziyat Mitzrayim is Sukkoht. This lasts seven days.
(טו) וּסְפַרְתֶּם לָכֶם מִמָּחֳרַת הַשַּׁבָּת מִיּוֹם הֲבִיאֲכֶם אֶת עֹמֶר הַתְּנוּפָה שֶׁבַע שַׁבָּתוֹת תְּמִימֹת תִּהְיֶינָה.
(טז) עַד מִמָּחֳרַת הַשַּׁבָּת הַשְּׁבִיעִת תִּסְפְּרוּ חֲמִשִּׁים יוֹם וְהִקְרַבְתֶּם מִנְחָה חֲדָשָׁה לַיהוָה.
(15) And ye shall count unto you from the morrow after the day of rest, from the day that ye brought the sheaf of the waving; seven weeks shall there be complete;
(16) even unto the morrow after the seventh week shall ye number fifty days; and ye shall present a new meal-offering unto the LORD.
(לד) דַּבֵּר אֶל בְּנֵי יִשְׂרָאֵל לֵאמֹר בַּחֲמִשָּׁה עָשָׂר יוֹם לַחֹדֶשׁ הַשְּׁבִיעִי הַזֶּה חַג הַסֻּכּוֹת שִׁבְעַת יָמִים לַיהֹוָה.
(לה) בַּיּוֹם הָרִאשׁוֹן מִקְרָא קֹדֶשׁ כָּל מְלֶאכֶת עֲבֹדָה לֹא תַעֲשׂוּ.
(לו) שִׁבְעַת יָמִים תַּקְרִיבוּ אִשֶּׁה לַיהוָה בַּיּוֹם הַשְּׁמִינִי מִקְרָא קֹדֶשׁ יִהְיֶה לָכֶם וְהִקְרַבְתֶּם אִשֶּׁה לַיהוָה עֲצֶרֶת הִוא כָּל מְלֶאכֶת עֲבֹדָה לֹא תַעֲשׂוּ.
(34) Speak unto the children of Israel, saying: On the fifteenth day of this seventh month is the feast of tabernacles for seven days unto the LORD.
(35) On the first day shall be a holy convocation; ye shall do no manner of servile work.
(36) Seven days ye shall bring an offering made by fire unto the LORD; on the eighth day shall be a holy convocation unto you; and ye shall bring an offering made by fire unto the LORD; it is a day of solemn assembly; ye shall do no manner of servile work.
(ד) וְעָמְדוּ רַגְלָיו בַּיּוֹם הַהוּא עַל הַר הַזֵּתִים אֲשֶׁר עַל פְּנֵי יְרוּשָׁלִַם מִקֶּדֶם וְנִבְקַע הַר הַזֵּיתִים מֵחֶצְיוֹ מִזְרָחָה וָיָמָּה גֵּיא גְּדוֹלָה מְאֹד וּמָשׁ חֲצִי הָהָר צָפוֹנָה וְחֶצְיוֹ נֶגְבָּה.
(ה) וְנַסְתֶּם גֵּיא הָרַי כִּי יַגִּיעַ גֵּי הָרִים אֶל אָצַל וְנַסְתֶּם כַּאֲשֶׁר נַסְתֶּם מִפְּנֵי הָרַעַשׁ בִּימֵי עֻזִּיָּה מֶלֶךְ יְהוּדָה וּבָא יְהוָה אֱלֹהַי כָּל קְדֹשִׁים עִמָּךְ.
(4) And His feet shall stand in that day upon the mount of Olives, Which is before Jerusalem on the east, And the mount of Olives shall cleft in the midst thereof Toward the east and toward the west, So that there shall be a very great valley; And half of the mountain shall remove toward the north, And half of it toward the south.
(5) And ye shall flee to the valley of the mountains; For the valley of the mountains shall reach unto Azel; Yea, ye shall flee, like as ye fled from before the earthquake In the days of Uzziah king of Judah; And the LORD my God shall come, And all the holy ones with Thee.
(ט) אֵין בָּאָרוֹן רַק שְׁנֵי לֻחוֹת הָאֲבָנִים אֲשֶׁר הִנִּחַ שָׁם מֹשֶׁה בְּחֹרֵב אֲשֶׁר כָּרַת יְהוָה עִם בְּנֵי יִשְׂרָאֵל בְּצֵאתָם מֵאֶרֶץ מִצְרָיִם. (י) וַיְהִי בְּצֵאת הַכֹּהֲנִים מִן הַקֹּדֶשׁ וְהֶעָנָן מָלֵא אֶת בֵּית יְהוָה.
(יא) וְלֹא יָכְלוּ הַכֹּהֲנִים לַעֲמֹד לְשָׁרֵת מִפְּנֵי הֶעָנָן כִּי מָלֵא כְבוֹד יְהוָה אֶת בֵּית יְהוָה. (יב) אָז אָמַר שְׁלֹמֹה יְהוָה אָמַר לִשְׁכֹּן בָּעֲרָפֶל. (יג) בָּנֹה בָנִיתִי בֵּית זְבֻל לָךְ מָכוֹן לְשִׁבְתְּךָ עוֹלָמִים.
(9) There was nothing in the ark save the two tables of stone which Moses put there at Horeb, when the LORD made a covenant with the children of Israel when they came out of the land of Egypt. (10) And it came to pass, when the priests were come out of the holy place, that the cloud filled the house of the LORD,
(11) so that the priests could not stand to minister by reason of the cloud; for the glory of the LORD filled the house of the LORD. (12) Then spoke Solomon: The LORD hath said that He would dwell in the thick darkness. (13) I have surely built Thee a house of habitation, A place for Thee to dwell in for ever.
God desires an abode in this world, this abode is the Jewish people. God’s presence is manifest in the Jewish people's life through holidays. The Sukkah is a physical representation of Gods presence,protection and providence in this world made possible through physical means that is why it is 7 seven days.
God wishes to be known through nature, through the number seven. Through the name Elokim which is equivalent in Gematria to Teva or nature. We read Kohelet on Sukkoht, the Safer calls Hashem Elokim.
The Zohar teaches, only through the natural order are miracles manifest. This is the secret behind the seven years Yackov had to work for Leah then Rachel. In order to understand the Drasha you must go through the Pshat.
I will use one aspect from each of the Haftorot for Sukkot.
Earthquakes: The physical manifestation of God through nature. (Source 5 )
The Beis Hamikdash: God’s abode in this world (Source 6 )