To experience that higher reality, Avraham had to travel throughout its physical counterpart. Similarly, when the Jews left Egypt, they needed to travel a spiritual road which would lead them not just to a physical place called Har Sinai, but to its spiritual doppelganger as well. The Jewish People needed to travel through a desert because they needed to become like the desert, devoid of preconceptions, unencumbered by the spiritual baggage of Egypt. Sitting on the beach would never have brought them to that spiritual state. The month of Sivan is associated with the planet Mercury.
Mercury symbolizes communication.
Thus it is that the Torah was given in the month of Sivan. Because The Torah is the Ultimate Communication. The Torah is the Ultimate Message. Thus it can only be received by way of a journey. The seven weeks of journeying in the desert, from Egypt to Sinai, are a paradigm of the Ultimate Communication from There to here.