The Talmud discusses the exact chronology of the Israelites' arrival at Sinai, establishing that they came on Rosh Chodesh Sivan (the new moon of Sivan) and that the Torah was given on the sixth or seventh of Sivan — making erev Rosh Chodesh Sivan the final moment before this sacred sequence began.
תָּא שְׁמַע: נִיסָן שֶׁבּוֹ יָצְאוּ יִשְׂרָאֵל מִמִּצְרַיִם, בְּאַרְבָּעָה עָשָׂר שָׁחֲטוּ פִּסְחֵיהֶם, וּבַחֲמִשָּׁה עָשָׂר יָצְאוּ, וְלָעֶרֶב לָקוּ בְּכוֹרוֹת. לָעֶרֶב סָלְקָא דַּעְתָּךְ?! אֶלָּא: מִבָּעֶרֶב לָקוּ בְּכוֹרוֹת, וְאוֹתוֹ הַיּוֹם חֲמִישִׁי בַּשַּׁבָּת הָיָה. מִדַּחֲמֵיסַר בְּנִיסָן חַמְשָׁא בְּשַׁבָּא, רֵישׁ יַרְחָא דְאִיָּיר שַׁבְּתָא, וְרֵישׁ יַרְחָא דְסִיוָן חַד בְּשַׁבָּת, קַשְׁיָא לְרַבָּנַן! אָמְרִי לָךְ רַבָּנַן: אִיָּיר דְּהַהִיא שַׁתָּא עַבּוֹרֵי עַבְּרוּהּ. תָּא שְׁמַע דְּלָא עַבְּרוּהּ נִיסָן שֶׁבּוֹ יָצְאוּ יִשְׂרָאֵל מִמִּצְרַיִם: בְּאַרְבָּעָה עָשָׂר שָׁחֲטוּ פִּסְחֵיהֶם, בַּחֲמִשָּׁה עָשָׂר יָצְאוּ, וְלָעֶרֶב לָקוּ בְּכוֹרוֹת. לָעֶרֶב סָלְקָא דַּעְתָּךְ?! אֶלָּא אֵימָא: מִבָּעֶרֶב לָקוּ בְּכוֹרוֹת. וְאוֹתוֹ הַיּוֹם חֲמִישִׁי בַּשַּׁבָּת הָיָה. הִשְׁלִים נִיסָן וְאֵירַע אִיָּיר לִהְיוֹת בַּשַּׁבָּת. חָסַר אִיָּיר, וְאֵירַע סִיוָן לִהְיוֹת בְּאֶחָד בַּשַּׁבָּת — קַשְׁיָא לְרַבָּנַן! הָא מַנִּי — רַבִּי יוֹסֵי הִיא.
Come and hear an additional proof with regard to the day of the revelation at Sinai from what was taught in a baraita: In the month of Nisan during which the Jewish people left Egypt, on the fourteenth, they slaughtered their Paschal lambs; on the fifteenth, they left Egypt; and in the evening, the firstborn were stricken. The Gemara asks: Does it enter your mind to say that they were stricken in the evening? Was the Plague of the Firstborn after the Jews left Egypt? Rather, say that the evening before, the firstborn were stricken. And that day was the fifth day of the week. From the fact that the fifteenth of Nisan was a Thursday, the New Moon of Iyyar was Shabbat, as Nisan is typically thirty days long. And the New Moon of Sivan was on the first day of the week, as Iyyar is typically twenty-nine days long. This is difficult according to the opinion of the Rabbis, who hold that the New Moon of Sivan that year was on Monday. The Gemara answers: The Rabbis could have said to you that a day was added to Iyyar that year and it was thirty days long. The New Moon was determined by testimony of witnesses who saw the new moon, together with astronomical calculations that the testimony was feasible. Therefore, Iyyar could be thirty days long. If that was the case, the New Moon of Sivan was on Monday. Come and hear an objection from what was taught in a different baraita that they did not add a day to Iyyar that year, as the Sages taught: In the month of Nisan during which the Jewish people left Egypt, on the fourteenth, they slaughtered their Paschal lambs; on the fifteenth, they left Egypt; and in the evening, the firstborn were stricken. The Gemara asks: Does it enter your mind to say that they were stricken in the evening? Was the Plague of the Firstborn after the Jews left Egypt? Rather, say that the evening before, the firstborn were stricken. And that day was the fifth day of the week. Nisan was complete, i.e., it was thirty days long, and the New Moon of Iyyar occurred on a Shabbat. Iyyar was lacking, i.e., it was twenty-nine days long, and the New Moon of Sivan occurred on the first day of the week. This is difficult according to the opinion of the Rabbis. The Gemara answers: Whose is the opinion in this baraita? It is the opinion of Rabbi Yosei. Therefore, this baraita poses no difficulty to the opinion of the Rabbis.