שִׁבְעָ֥ה שָׁבֻעֹ֖ת תִּסְפָּר־לָ֑ךְ מֵהָחֵ֤ל חֶרְמֵשׁ֙ בַּקָּמָ֔ה תָּחֵ֣ל לִסְפֹּ֔ר שִׁבְעָ֖ה שָׁבֻעֽוֹת׃י וְעָשִׂ֜יתָ חַ֤ג שָׁבֻעוֹת֙ לַה׳ אֱלֹקֶ֔יךָ מִסַּ֛ת נִדְבַ֥ת יָדְךָ֖ אֲשֶׁ֣ר תִּתֵּ֑ן כַּאֲשֶׁ֥ר יְבָרֶכְךָ֖ ה׳ אֱלֹקֶֽיךָ׃
You shall count off seven weeks; start to count the seven weeks when the sickle is first put to the standing grain. Then you shall observe the Feast of Weeks for the LORD your God, offering your freewill contribution according as the LORD your God has blessed you.
וַתִּתֶּן לָנוּ ה׳ אֱלקֵינוּ בְּאַהֲבָה לשבת שַׁבָּתות לִמְנוּחָה ו מועֲדִים לְשמְחָה חַגִּים וּזְמַנִּים לְששון אֶת יום חַג הַשָׁבוּעות הַזֶּה זְמַן מַתַּן תּורָתֵינוּ:
You have given us, O Lord our God, in love Shabbat to rest on, festivals to celebrate on, holidays and times to rejoice on this festival of Shavuot the time of the giving of the Torah.
תנו רבנן בששי בחדש ניתנו עשרת הדברות לישראל רבי יוסי אומר בשבעה בו
The Sages taught: On the sixth day of the month of Sivan, the Ten Commandments were given to the Jewish people. Rabbi Yosei says: On the seventh day of the month.
Rav Shimshon Rafael Hirsch (commentary to Vayikra 23:21)
The essence of Shavuot is not the giving of the Torah but the preparedness of man to accept the Torah. Just as the Jews in the desert prepared themselves to accept the Torah, so must we. This would alleviate the difficulty of assigning the date of the holiday to the sixth day of the month, which is not necessarily the day the Torah was given, but was, in fact, the day the People of Israel prepared themselves to receive it. This understanding is borne out by the choice of Torah reading for Shavuot, Chapter 19 of Exodus, which begins with the preparations made to receive the Torah.
בַּחֹ֙דֶשׁ֙ הַשְּׁלִישִׁ֔י לְצֵ֥את בְּנֵי־יִשְׂרָאֵ֖ל מֵאֶ֣רֶץ מִצְרָ֑יִם בַּיּ֣וֹם הַזֶּ֔ה בָּ֖אוּ מִדְבַּ֥ר סִינָֽי׃
On the third new moon after the Israelites had gone forth from the land of Egypt, on that very day, they entered the wilderness of Sinai.
ביום הזה. בְּרֹאשׁ חֹדֶשׁ; לֹא הָיָה צָרִיךְ לִכְתֹּב אֶלָּא בַּיּוֹם הַהוּא, מַהוּ בַּיּוֹם הַזֶּה? שֶׁיִּהְיוּ דִּבְרֵי תוֹרָה חֲדָשִׁים עָלֶיךָ כְּאִלּוּ הַיּוֹם נְתָנָם (ברכות ס"ג):
ביום הזה THE SAME (lit., this) DAY — on the day of the New Moon. (Mekhilta d'Rabbi Yishmael 19:1:3; Shabbat 86b). It ought not to write ביום הזה, but ביום ההוא, “on that day”; what, then, is the force of the words “on this day”? Since they refer to the day when the Israelites came to Sinai to receive the Torah they imply that the commands of the Torah should be to you each day as something new (not antiquated and something of which you have become tired), as though He had only given them to you for the first time on the day in question (Yalkut Shimoni on Torah 273; cf. Berakhot 63b).
Rabbi Beinish Ginsburg, Meiafailah L'Or Gadol: Insights into Pesach, Sefiras HaOmer, and Shavuos, page 110
When a Jew thinks of a lulav, right away he thinks of Sukkos. When a Jew thinks of matza, right away he thinks of Pesach. But when a Jew thinks of Matan Torah, Hashem does not want us to focus only on Shavuos. No- Matan Torah applies every day of the year, at all times. We should think of every day as Yom Matan Torah. Therefore, the Akeidas Yitzchak explains, the Torah purposely de-emphasizes the link between Shavuos and Matan Torah so that we do not focus on Matan Torah only on Shavuos.
יְהֹוָ֗ה אֶ֤רֶךְ אַפַּ֙יִם֙ וְרַב־חֶ֔סֶד נֹשֵׂ֥א עָוֺ֖ן וָפָ֑שַׁע וְנַקֵּה֙ לֹ֣א יְנַקֶּ֔ה פֹּקֵ֞ד עֲוֺ֤ן אָבוֹת֙ עַל־בָּנִ֔ים עַל־שִׁלֵּשִׁ֖ים וְעַל־רִבֵּעִֽים׃
‘יהוה ! slow to anger and abounding in kindness; forgiving iniquity and transgression; yet not remitting all punishment, but visiting the iniquity of parents upon children, upon the third and fourth generations.’