Q. Why do Ashkenazim begin selichot (penitential prayers) a minimum of four days before Rosh HaShanah?
A. Possibly because our prayers on Rosh HaShanah and Yom Kippur show a person the need for self-sacrifice for the sake of God.
In Temple times a sacrifice had to be set aside a minimum of four days in advance. This ensured that the animal was in a fit state for the sacrificial ritual.
By way of analogy, the selichot prayers help us to be spiritually ready at least four days before Rosh HaShanah – not that we sacrifice ourselves in a literal sense but we have to be able to put ourselves on the meeting table for assessment and judgment.