Every child learns the question in Jewish day school. If the sukkah reminds us of God’s protection of the Jewish people in the desert why don’t we build it in the month of Nisan when the Jewish people left Egypt. There are many answers but one that Rav Yitzchok Hutner gives in his book Pachad Yitzchak I find particularly meaningful. One opinion in the Talmud is that the sukkah represents the Divine cloud with which God protected the Jews in the desert. In the bible this cloud left the Jews after their sin worshiping the golden calf and returned after the erection of the tabernacle.
Rav Hutner writes that the Tabernacle was begun five days after Moses returned with the second set of Tablets on Yom Kippur –namely the beginning of Sukkot. Thus the sukkah represents not the Divine presence that protected the Jewish people in the desert immediately but the cloud that returned after their sin and repentance. This divine presence which emerged a second time only after the sin of the Jewish people was much more powerful perhaps than that before their sin. Indeed Rav Hutner says, this is why Sukkot in particular is called the holiday of joy. Though all mitvot are a source of holy joy, it is tishuvah, repentance that brings the most organic, the most internal, the deepest most personal joy.
Much blessing for a joyous end of sukkot and a wild simchat Torah!