The verse (Vayikra 23:40) states concerning the taking of the four species on the first day of Sukkot:
“And you shall take for yourselves on the first day, the fruit of the hadar tree, date palm fronds, a branch of a braided tree, and willows of the brook, and you shall rejoice before the Lord your God for a seven day period.”
The Medrash (Tanchuma, Emor 23) asks a simple question: “Why is the first day of Sukkot considered the first day, when it is really the 15th day of the month?”
Its answer: “It is the first day of reckoning of sin.”
Indeed the Medrash (Vayikra Rabba, Emor 30:6) explains, that until the holiday of Sukkot, the Jewish people are involved with their Sukkot and their lulavim and therefore literally have no time to sin.