The First Mitzvah—Fixing the New month
The Torah was given to bring sanctity to the world. Each time a mitzvah is observed this goal is brought one stage closer, as another place and another moment becomes holy.
The mitzvah causes holiness to be felt in two dimensions: space and time, but most mitzvos are limited to a specific place or time. However, the mitzvah of fixing the new month is the sanctification of time itself, for every moment within a given month is dependent on the exact time which that month begins.
Time is even more general and all-encompassing than space, since: a.) Time was created before space, and, b.) No place can exist outside time (see Hemshech Ayin Beis vol. 1, p. 339).
Thus, the most generic of all mitzvos is the fixing of the new month, which is why it was written first.
(Based on Likutei Sichos vol. 26, p. 59ff.)