Did God require a sacrifice to forgive the sins of mankind?

Yes.

This is perhaps one of the simplest questions to answer. The New Testament makes it clear that the Old Testament sacrifices were only shadows of what God really wanted. Such as in “Sacrifices and offerings you have not desired” (Hebrews 10:5). But nevertheless, the final sacrifice, the submission of Jesus to his father’s will, was still required:

And walk in love, as Christ loved us and gave himself up for us, a fragrant offering and sacrifice to God. (Ephesians 5:2 ESV)

But when Christ had offered for all time a single sacrifice for sins, he sat down at the right hand of God, (Hebrews 10:12)

So clearly a sacrifice took place, and was needed. But the ‘Yes’ does not really tell us ‘Why’.

There is little in the Bible about ‘propitiation’, the idea – deeply rooted in the Ancient Near East – of sacrifice appeasing the wrath of God. In 1 John 2:2 and 4:10 Christ is called the “propitiation for our sins.” So clearly that is one aspect of a multi-faceted view of Christ’s sacrifice. One part of the picture. But given that God himself gave his son, Jesus, because he loved the world (John 3:16), this is a very different kind of ‘propitiation’ from the appeasement required by the pagan gods of old.

In the New Testament the sacrifice is prepared and given by God himself, to men, for men. This is not something that Christ initiated to win the favour of God, on the contrary this sacrifice was something that God himself had not only initiated, but in fact God had foreknown since before the foundation of the world:

…names have not been written in the Book of Life of the Lamb slain from the foundation of the world. (Revelation 13:8)

…but with the precious blood of Christ, as of a lamb without blemish and without spot  (1 Peter 1:19)

So the sacrifice is to change men, not to change God. It is to reconcile men to God, not to reconcile God to men. Therefore this sacrifice also requires a response from Christians, to honour it in their lives.

For if we go on sinning deliberately after receiving the knowledge of the truth, there no longer remains a sacrifice for sins, (Hebrews 10:26)