Meaning of the Omer, Counting, and Shavuot

Was Shavuot the same time as Matan Torah? It is supposed to be the 50th day- after the first day of Pesach. Shavuot did not always take place on a fixed date – when calendar wasn’t fixed, the day could vary, just as the number of days in the preceding months could vary. In the Torah, Shavuot is always described in agricultural terms - the only regel (pilgrimage holiday) not to be explicitly linked with a historical commemoration. Did Hazal (the Rabbinic Sages) simply decide to link Shavuot with the Giving of the Torah, or are there strong hints within the Torah as well? If so, why are they not explicitly linked? What can we understand - and what are we meant to appreciate about Shavuot from the way the Torah describes the commandments surrounding Shavuot?