Shavuot isn't about Sinai

The LORD spoke to Moses, saying: Speak to the Israelite people and say to them: These are My fixed times, the fixed times of the LORD, which you shall proclaim as sacred occasions. On six days work may be done, but on the seventh day there shall be a sabbath of complete rest, a sacred occasion. You shall do no work; it shall be a sabbath of the LORD throughout your settlements. These are the set times of the LORD, the sacred occasions, which you shall celebrate each at its appointed time: In the first month, on the fourteenth day of the month, at twilight, there shall be a passover offering to the LORD, and on the fifteenth day of that month the LORD’s Feast of Unleavened Bread. You shall eat unleavened bread for seven days. On the first day you shall celebrate a sacred occasion: you shall not work at your occupations. Seven days you shall make offerings by fire to the LORD. The seventh day shall be a sacred occasion: you shall not work at your occupations. The LORD spoke to Moses, saying: Speak to the Israelite people and say to them: When you enter the land that I am giving to you and you reap its harvest, you shall bring the first sheaf of your harvest to the priest. He shall elevate the sheaf before the LORD for acceptance in your behalf; the priest shall elevate it on the day after the sabbath. On the day that you elevate the sheaf, you shall offer as a burnt offering to the LORD a lamb of the first year without blemish. The meal offering with it shall be two-tenths of a measure of choice flour with oil mixed in, an offering by fire of pleasing odor to the LORD; and the libation with it shall be of wine, a quarter of a hin. Until that very day, until you have brought the offering of your God, you shall eat no bread or parched grain or fresh ears; it is a law for all time throughout the ages in all your settlements. And from the day on which you bring the sheaf of elevation offering—the day after the sabbath—you shall count off seven weeks. They must be complete: you must count until the day after the seventh week—fifty days; then you shall bring an offering of new grain to the LORD. You shall bring from your settlements two loaves of bread as an elevation offering; each shall be made of two-tenths of a measure of choice flour, baked after leavening, as first fruits to the LORD. With the bread you shall present, as burnt offerings to the LORD, seven yearling lambs without blemish, one bull of the herd, and two rams, with their meal offerings and libations, an offering by fire of pleasing odor to the LORD. You shall also offer one he-goat as a sin offering and two yearling lambs as a sacrifice of well-being. The priest shall elevate these—the two lambs—together with the bread of first fruits as an elevation offering before the LORD; they shall be holy to the LORD, for the priest. On that same day you shall hold a celebration; it shall be a sacred occasion for you; you shall not work at your occupations. This is a law for all time in all your settlements, throughout the ages. And when you reap the harvest of your land, you shall not reap all the way to the edges of your field, or gather the gleanings of your harvest; you shall leave them for the poor and the stranger: I the LORD am your God. The LORD spoke to Moses, saying: Speak to the Israelite people thus: In the seventh month, on the first day of the month, you shall observe complete rest, a sacred occasion commemorated with loud blasts. You shall not work at your occupations; and you shall bring an offering by fire to the LORD. The LORD spoke to Moses, saying: Mark, the tenth day of this seventh month is the Day of Atonement. It shall be a sacred occasion for you: you shall practice self-denial, and you shall bring an offering by fire to the LORD; you shall do no work throughout that day. For it is a Day of Atonement, on which expiation is made on your behalf before the LORD your God. Indeed, any person who does not practice self-denial throughout that day shall be cut off from his kin; and whoever does any work throughout that day, I will cause that person to perish from among his people. Do no work whatever; it is a law for all time, throughout the ages in all your settlements. It shall be a sabbath of complete rest for you, and you shall practice self-denial; on the ninth day of the month at evening, from evening to evening, you shall observe this your sabbath. The LORD spoke to Moses, saying: Say to the Israelite people: On the fifteenth day of this seventh month there shall be the Feast of Booths to the LORD, [to last] seven days. The first day shall be a sacred occasion: you shall not work at your occupations; seven days you shall bring offerings by fire to the LORD. On the eighth day you shall observe a sacred occasion and bring an offering by fire to the LORD; it is a solemn gathering: you shall not work at your occupations. Those are the set times of the LORD that you shall celebrate as sacred occasions, bringing offerings by fire to the LORD—burnt offerings, meal offerings, sacrifices, and libations, on each day what is proper to it— apart from the sabbaths of the LORD, and apart from your gifts and from all your votive offerings and from all your freewill offerings that you give to the LORD. Mark, on the fifteenth day of the seventh month, when you have gathered in the yield of your land, you shall observe the festival of the LORD [to last] seven days: a complete rest on the first day, and a complete rest on the eighth day. On the first day you shall take the product of hadar trees, branches of palm trees, boughs of leafy trees, and willows of the brook, and you shall rejoice before the LORD your God seven days. You shall observe it as a festival of the LORD for seven days in the year; you shall observe it in the seventh month as a law for all time, throughout the ages. You shall live in booths seven days; all citizens in Israel shall live in booths, in order that future generations may know that I made the Israelite people live in booths when I brought them out of the land of Egypt, I the LORD your God. So Moses declared to the Israelites the set times of the LORD.

On the third day of the week, God said to them the mitzva of setting boundaries around Mount Sinai. On the fourth day of the week, the husbands and wives separated from one another. And the Rabbis hold: On the second day of the week the New Moon was established, and on the second day of the week God did not say anything to them due to the weariness caused by their journey. On the third day of the week, God said to them: “And you shall be to Me a kingdom of priests and a holy nation; these are the words that you shall speak to the children of Israel” (Exodus 19:6). On the fourth day of the week, God said to them the mitzva of setting boundaries around Mount Sinai. On the fifth day of the week, the husbands and wives separated from one another. The Gemara raises an objection: Doesn’t the verse state: “And the Lord said to Moses: Go to the people and sanctify them today and tomorrow and let them wash their garments” (Exodus 19:10), indicating that the husbands and wives were separated for only two days? This is difficult according to the opinion of Rabbi Yosei, who said earlier that the separation was for three days. The Gemara answers: Rabbi Yosei could have said to you: Moses added one day to the number of days that God commanded based on his own perception

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.