The Gemara (Shabbat 86b) records a disagreement between the Rabbanan and Rabbi Yosi as to the day of the month of Sivan that the Aseret ha-Dibrot were handed down at Sinai. The first opinion is that it occurred on the sixth of the month while Rabbi Yosi maintains that it occurred on the seventh. The Gemara goes on to explain that both agree on two matters: first, that the Bnai Yisrael arrived in the Sinai desert on the first of that month and, second, that the Torah was given on a Shabbat. They disagree, however, continues the Gemara, regarding on what day of the week did the first of the month fall, on a Sunday (in which case the Torah was given on the seventh of the month) or on a Monday (in which case the Torah was given on the sixth).
A second Gemara. The Gemara (Shabbat 87b) informs us that the Bnai Yisrael left Egypt on a Thursday.
A third Gemara. The Gemara (Pesachim 68b) simply assumes that the holiday of Shavuot commemorates the day of the giving of the Torah. This is not self-evident because the Torah refers to this holiday four times and not once makes this association. In Shemot 23:16 it is referred to as “chag ha-asif,” in Shemot 34:22 as “chag shavuot,” in Bamidbar 28:26 as “yom ha-bikkurim,” and in Devarim 15:9, 16 as “chag shavuot.” Nowhere does the Torah associate this holiday with the event of Revelation, an association that became self-evident in later rabbinic literature. Indeed, in his biblical commentary on Vayikra 23, the Abravanel wonders (question #17) why the Torah does not explicitly make this connection, and he is only one of many who address this issue.
And a pasuk. The Torah (Vayikra 23:15-21) tells us that fiftieth day from the beginning of the counting of the omer is a holiday and the clear assumption in Jewish tradition is that this is a reference to the holiday of Shavuot.