I agree with this, except that Jesus did sacrifice, his sacrifice was his life, meaning his whole life. He laid down his life for the living God. Not doing his will, but doing Gods will. Bringing the gospel and spreading the word and those who repent, believe and have faith would be saved. He was a living sacrifice. He was dead to the flesh but he was alive in God and full of the spirit.
Jesus was saving before he went on the cross, and we are saved from our past sins through repentance and faith and then we are to turn from wilful sinning, and it says in the Bible that we are saved by his life, death doesn't save, life saves.
Luke 7
And he said to the woman, Thy faith hath saved thee; go in peace.
Luke 18
And Jesus said unto him, Receive thy sight: thy faith hath saved thee
Romans 5
For if, when we were enemies, we were reconciled to God by the death of his Son, much more, being reconciled, we shall be saved by his life.
Jesus also said,
Matthew 16
For whosoever will save his life shall lose it: and whosoever will lose his life for my sake shall find it.
To lose our life is death to self, and to do this we must take up our cross, deny ourselves as follow Jesus. If we don't take up our cross, Jesus said that were not worthy him.
Romans 6
What shall we say then? Shall we continue in sin, that grace may abound?
God forbid. How shall we, that are dead to sin, live any longer therein?
Know ye not, that so many of us as were baptized into Jesus Christ were baptized into his death? Therefore we are buried with him by baptism into death: that like as Christ was raised up from the dead by the glory of the Father, even so we also should walk in newness of life.
Jesus is the way, the truth and the life, and if we are his and raised with him then we will walk in newness of life.
1 John 2
But whoso keepeth his word, in him verily is the love of God perfected: hereby know we that we are in him. He that saith he abideth in him ought himself also so to walk, even as he walked.