Question Restatement: How is Jesus' declaration, to forgive sins, reconciled with the previous sacrificial system.
If I understand this question, this question has multiple parts, (*I think):
- Was it necessary for Jesus to verbally state that they were forgiven, and if not, why did he do it?
- Jesus' authority to forgive sins;
- Whether the shedding of blood is required for forgiveness.
Why Did Jesus Publicly Pronounce Forgiveness?
Technically, forgiveness is a legal thing, (the cancellation of debt), and witnesses are needed for such acts.
2 Cor. 13:1, NASB - This is the third time I am coming to you. Every fact is to be confirmed by the testimony of two or three witnesses.
However, this does not answer why Jesus didn't just say this to this man, with only his disciples present.
Answer, Part 1: The text states that Jesus knew exactly what was on their heart, and intentionally provoked them until there would be a "crux", a point at which there could be no resolution through debate, (whether he had authority to forgive sins)--and people would either believe, seeing the Power of God, or reject him, under the Wisdom and Traditions of Men :
Luke 5:20-26, NASB - 20 Seeing their faith, He said, “Friend, your sins are forgiven you.” 21 The scribes and the Pharisees began to reason, saying, “Who is this man who speaks blasphemies? Who can forgive sins, but God alone?” 22 But Jesus, aware of their reasonings, answered and said to them, “Why are you reasoning in your hearts? 23 Which is easier, to say, ‘Your sins have been forgiven you,’ or to say, ‘Get up and walk’? 24 But, so that you may know that the Son of Man has authority on earth to forgive sins,”—He said to the paralytic—“I say to you, get up, and pick up your stretcher and go home.” 25 Immediately he got up before them, and picked up what he had been lying on, and went home glorifying God. 26 They were all struck with astonishment and began glorifying God; and they were filled with fear, saying, “We have seen remarkable things today.”
1 Cor. 2:4, NASB - and my message and my preaching were not in persuasive words of wisdom, but in demonstration of the Spirit and of power, 5 so that your faith would not rest on the wisdom of men, but on the power [δυνάμεως] of God.
John 10:38, NASB - but if I do them, though you do not believe Me, believe the works, so that you may know and understand that the Father is in Me, and I in the Father.”
Reconciliation Jesus' Authority as High Priest
The Christian texts assert that forgiveness is officiated, by the Great High Priest, and the perfect sacrifice offered once and for all--no longer having to continue offering up imperfect Sacrifices.
Answer, Part 2 - From the Christian point of view, as the former law only "foreshadowed" this "heavenly/eternal" priestly service, Jesus' service as High Priest fulfills the Eternal requirements, and so would have authority, and fulfilled any temporal requirements reflected in the Law of Moses--which was only temporary.
Hebrews 8:1-6, NASB - 8 Now the main point in what has been said is this: we have such a high priest, who has taken His seat at the right hand of the throne of the Majesty in the heavens, 2 a minister in the sanctuary and in the true tabernacle, which the Lord pitched, not man. 3 For every high priest is appointed to offer both gifts and sacrifices; so it is necessary that this high priest also have something to offer. 4 Now if He were on earth, He would not be a priest at all, since there are those who offer the gifts according to the Law; 5 who serve a copy and shadow of the heavenly things, just as Moses was warned by God when he was about to erect the tabernacle; for, “See,” He says, “that you make all things according to the pattern which was shown you on the mountain.” 6 But now He has obtained a more excellent ministry, by as much as He is also the mediator of a better covenant, which has been enacted on better promises.
Hebrews 9:11-14, NASB - But when Christ appeared as a high priest of the good things to come, He entered through the greater and more perfect tabernacle, not made with hands, that is to say, not of this creation; 12 and not through the blood of goats and calves, but through His own blood, He entered the holy place once for all, having obtained eternal redemption. 13 For if the blood of goats and bulls and the ashes of a heifer sprinkling those who have been defiled sanctify for the cleansing of the flesh, 14 how much more will the blood of Christ, who through the eternal Spirit offered Himself without blemish to God, cleanse your conscience from dead works to serve the living God?
Sacrifice isn't Necessary for Forgiveness
The Jewish viewpoint is that there seems to be misunderstanding regarding the "previous" Sacrificial system--the way Jews today perceive it as well. See Atonement in the Absence of Sacrifices?
In exceptional circumstances, prayer was sufficient to find forgiveness, when the Temple/High priest were unavailable.
This is not at all incompatible with the Christian Point of View, that forgiveness was possible without blood sacrifice. John the Baptist preached the "Gospel"--repentance for the forgiveness of sins--even before Jesus began his ministry, (Mark 1:4, Luke 3:3, Acts 2:38).
In 1 Kings, 8:37, Solomon, very clearly, acknowledges that the Temple, and its sacrifices are unnecessary for forgiveness.
Answer, Part 3: If Jesus did know the heart of the person he was speaking to, he could legitimately say, and recognize, that they had been forgiven, under 1 Kings 8, and the "disaster of the Roman Occupation"--without the necessity of a sacrifice, or even looking forwards to him being the sacrifice.
1 Kings 8:46-50 - 46 “When they sin against You (for there is no man who does not sin) and You are angry with them and deliver them to an enemy, so that they take them away captive to the land of the enemy, far off or near; 47 if they take thought in the land where they have been taken captive, and repent and make supplication to You in the land of those who have taken them captive, saying, ‘We have sinned and have committed iniquity, we have acted wickedly’; 48 if they return to You with all their heart and with all their soul in the land of their enemies who have taken them captive, and pray to You toward their land which You have given to their fathers, the city which You have chosen, and the house which I have built for Your name; 49 then hear their prayer and their supplication in heaven Your dwelling place, and maintain their cause, 50 and forgive Your people who have sinned against You and all their transgressions which they have transgressed against You, and make them objects of compassion before those who have taken them captive, that they may have compassion on them.
NOTE: Hebrews 9:23 seems to be the only exception in the New Testament, indicating that forgiveness cannot occur without "blood". But, this really should be addressed in another question. However, this passage can be reconciled in view of the passage/concept about the "Serpent being raised in the desert, (John 3:14)." Which speaks of "looking forward to," and beyond the "shadow/foreshadowing", etc; and also in view of the differences between purification, cleansing, and forgiveness.