There are four days between Yom Kippur and Sukkot, which is the biblical holiday that commands to make a Sukkah. Some bible scholars say that the influence of Yom Kippur and its power to expiate sins extends into these four days. Just as before Rosh Hashana we are given a minimum of four days of Selichot (prayers for forgiveness and mercy) in order to prepare ourselves to enter Rosh Hashana as a blemishless sacrifice, so too we are given four days after Yom Kippur to settle back to our real level into Sukkot. The accounting of our sins during these four days is then retroactively calculated according to the level we reach on the first day of Sukkot. The four days between Yom Kippur and Sukkot also correspond to the four letters of God’s Ineffable Name. Our feelings during these four days are raw material to be shaped in calm reflection, and transformed into our calculated service of God on the first days of Sukkot.
Hashem gave the Torah, even after the golden calf was made, on the Yom Kippur after the second Tablets of the Ten Commandments which illustrated Hashem granting us forgiveness . Right away He gave the commandment to make the Mishkan (The Tabernacle), which showed Hashem’s love for Israel because Hashem put His Shechinah amongst them. The Sukkah has the same message; all year we do mistakes like the golden calf, but then comes Yom Kippur- Hashem forgives us and then comes Sukkot where He tells us to make and sit in the Sukkah and “I will Protect you”. The connection is that Yom Kippur and Sukkot are connected in that they illustrate Hashem’s forgiveness of our Aveiros (the word comes from the Hebrew root ayin-bet-resh, meaning to pass or cross over with the implied meaning of transgressing from a moral boundary).
The Old Testament has several teachings and illustrations such as these, of how HaShem offers us forgiveness for our transgressions. The symbolism is very rich and significant, after all, if it’s in the Torah/Bible, it’s important and not to be ignored.