The acceptance of God's Kingship and purification of the Beit HaMikdash allow us to get close to Him in a spirit of joyfulness during the Festival of Sukkot.
Most of the sections in the Torah dealing with the Festivals group Sukkot together with Pesach and Shavuot as the Three Pilgrimage Festivals during which we are commanded to bring offerings in the Beit Hamikdash. However, in Numbers, chapters 28-29, Sukkot is grouped together with the Festivals of the seventh month. Sukkot is known as a time of joy, and the Torah stresses this by saying "… and you shall be altogether joyful." (Deut. 16:15). The connection between Sukkot as a Festival full of joy and the Days of Judgment at the beginning of the seventh month seems to be far-fetched and artificial.
Chapter 29, which describes the additional sacrifices, gives us new insight by grouping Sukkot together with the Festivals of Tishrei.
It would seem that the very name of the Festival indicates its membership in this group. The name of the Festival of Sukkot does not appear explicitly - "and on the fifteenth day of the seventh month" (29:12). In contrast to the other Festivals mentioned in this chapter, no special commandments are assigned to this Festival, thus the Torah stresses that the essence and identity of this Festival are mainly derived from its occurrence in the middle of the seventh month.
It would appear that, the fact that it occurs in the middle of the seventh month imbues it with central importance in this month of Festivals. The other Festivals occurring in this month last only one day, whereas this one lasts seven full days. On each day of this Festival we bring a different number of sacrifices. We can now explain that the Holy Days at the beginning of the month and on the tenth day are but days of preparation for the central part of the month. The Torah does not go into great detail here about the first day of the seventh month, yet from other verses we infer that this is the Day of Judgment and God's Kingship, and that the blowing is our anointment of God over us. Regarding Yom Kippur, we infer that the altar must be purified in advance of the grand celebrations which will shortly take place, we must atone and prepare the altar for the Festival.
Only after renewing our acceptance of God's Kingship and atoning and preparing the Mikdash, the altar and the Kohanim, can we celebrate the long, joyous Festival of the seventh month with a multitude of sacrifices. Therefore, on the fifteenth day of the seventh month, we celebrate our closeness to God in a spirit of joyfulness, after the Days of Judgment and preparation in which we were in a spirit of dread and fear.