Due to time constraints, we present the translation of this sicha as prepared by Sichos in English (available on their website):
Rosh Chodesh Sivan marks the day when the Bnei Yisrael came to the Sinai desert, midbar Sinai. This location was chosen by G-d as the fitting place for the Torah to be given, and therefore, immediately upon arriving, Moshe began preparing them to receive the Torah. This same connection between the place (midbar Sinai) and the event also finds expression in the fact that Parshas Bamidbar is always read before Shavuos.
There are two reasons given to explain why Parshas Bamidbar is always read before Shavuos. First of all, a midbar (desert) has no owner. Even a public domain has owners — it’s just that everyone owns it equally. In contrast, a desert has no owner whatsoever. The Torah was therefore given in a desert, to teach us that whoever wishes to receive the Torah is free to do so.
A second reason is connected with the curses of Parshas Bechukosai. The Gemara (Megillah 31b) says that since Shavuos is considered to be like the beginning of the year, Ezra established that these curses be read before Shavuos, “to finish the year and its curses.” According to this reason, Bamidbar is read before Shavuos to provide a respite between the curses and Shavuos.
Both of these reasons need explanation. According to the first reason, the Torah was given in a midbar to stress that the Torah is ownerless and that everyone has equal access to it. However, the Torah was given exclusively to the Jewish people! It would have seemed more fitting for it to be given in a private place, or at least a public place which was in the communal possession of all Jews.