An excerpt from my notes on the feasts of Israel
Sacrifice, of some kind, was required with the observance of every feast under the old covenant. The types and amounts of animals varied from feast to feast but generally there was a burnt offering and a sin offering. The main purpose of a burnt offering was to be “an aroma pleasing to the LORD” (Lev. 1:9, 13, 17). For this offering, the entire animal was burned on the altar. The sin offering was made to make atonement for the people (Lev. 4:20, 26, 31, 35). These offerings had to be made during every feast because of Israel’s continuing sinfulness. They could not relate to God or participate in His feasts unless sin was dealt with and God was satisfied.
Jesus’s one sacrifice was sufficient for all time and beyond. On the cross He fulfilled every burnt offering and sin offering pictured in the Old Testament. In Him, there is no need for repeated sacrifice. Why then is the cross pictured at every feast through the offerings that were commanded? It is because our participation in any aspect of Christ depends on the cross. We can only be united to His resurrection if we are united to His death (Rom. 6:5). Sharing His anointing depends on His atonement. And God couldn’t tabernacle or dwell in us unless His temple was destroyed and raised in three days (John 2:19-22).
It isn’t just that the cross is a first step that we have to start with. We cannot move on from the cross any more that a tree can move from its root or a building from its foundation. This is why, even in the type, the Lord keeps the cross continually before us. It is as if He is saying, “If I hadn’t died you would have no part in me” (cf. John 13:8).
Painting by Patrick Murphy: http://inspiredsketch.blogspot.com/