In the holiday amidah, we refer to Sukkot as zman simchatenu, the holiday of our joy. The actual commandment of Simchat Yom Tov, rejoicing on holidays, is mentioned in the Torah specifically regarding Sukkot (דברים פרק ט"ו פסוק י"ד). Similarly, after giving the commandment to take the four minim, the Torah states "ושמחתם לפני ה' א-לוהיכם שבעת ימים" "and you shall rejoice before Hashem your God seven days" (ויקרא פרק כ"ג פסוק מ'). In fact, Shlomo's famous party which he throws to celebrate the opening of the Bet HaMikdash (and which we read about on the second day of Sukkot and on Shemini Atzeret) took place over Sukkot (מלכים א' פרק ח' פסוקים ב', ס"ה-ס"ו). Why is such a strong element of joy within the holiday of Sukkot, as opposed to other holidays?
The Torah tells us that the reason for celebrating Sukkot is to remember that Hashem settled us in Sukkot when He took us out of Egypt, למען ידעו דרתיכם כי בסכות הושבתי את בני ישראל בהוציאי אותם מארץ מצרים, (ויקרא כג:מג). Chazal say that the 07 cows brought over the course of Sukkot for the mussaf represent the 07 nations of the world. The idea of non-Jewish nations having a part in Sukkot is also expressed in the first day's Haftarah, when the Navi states that in the end of days all the nations will observe Sukkot, and Hashem will deprive rain from any of the nations that don't observe it (זכריה יד:טז-יט). What type of connection is there suppose to be between non-Jewish nations and a holiday that was given to commemorate Hashem settling the Jews in Sukkot?