Until the night before the Exodus, time belonged to Egypt. The calendar that mattered was the calendar of Pharaoh, its new year set by the flooding of the Nile. Targum Pseudo-Jonathan on Exodus 12:2 tells Israel that from this month forward, a new clock starts. The Aramaic specifies what the calendar is for: festivals, appointed times, and cycles. From Nisan, the counting begins.
This is more radical than it first sounds. A slave does not own his time; his master decides when he rises and when he sleeps, which days are ordinary and which are holy. By assigning Israel its own calendar on the very eve of liberation, God gives the soon-to-be-freed people something that slaves do not possess: the authority to mark time. The Targum calls Nisan "the first of the number of the months of the year."
The Mishnah (Rosh Hashanah 1:1) later records that Nisan is still the first of the months for kings and festivals, even though Tishrei became the first of the year for agricultural and civil purposes. That duality reflects the verse's wisdom. Freedom has its own clock. Everyday life has another. Both are legitimate, but on the night of liberation, only one counts.
This is why Passover falls in Nisan and not in another month. The festival carries its own calendar with it. To celebrate Pesach is to stand in the month that reset all months.
Takeaway: The first gift of freedom is not land or power. It is the right to name your own days.