The answer to this question is actually a deep secret, which cannot be revealed openly.
After all, Esther herself asked Mordechai this very question. When will the story of the Megillah occur?
His answer, as recorded in Esther 4:14, was:
וּמִ֣י יוֹדֵ֔עַ אִם־לְעֵ֣ת כָּזֹ֔את הִגַּ֖עַתְּ
Who can know if you have yet come to the time?
i.e. the precise timing of the Purim story is destined to remain a mystery.
This, however, is all on the level of peshat. If we read the verse using the tools of remez, we can indeed know when the story is going to take place.
וּמִ֣י יוֹדֵ֔עַ אִם־לְעֵ֣ת כָּזֹ֔את הִגַּ֖עַתְּ
And [there will be a website called] Mi Yodeya. If it is this time, you will have arrived.
i.e. The Purim story is destined to occur once Mi Yodeya is up and running.
Thus, we can conclude that it happened on December 6th 2009.