First point, it doesn't say the Lamb 'offered Himself' for the sins of the world. You added this yourself.
John 1:29
The next day John seeth Jesus coming unto him, and saith, Behold the Lamb of God, which taketh away the sin of the world.
God desires mercy rather than any sacrifice. How does His mercy take away our sins?
It is the same exact way as in the OT.
2 Chronicles 7:14
If my people, which are called by my name, shall humble themselves, and pray, and seek my face, and turn from their wicked ways; then will I hear from heaven, and will forgive their sin, and will heal their land.
Jeremiah 26:13
Therefore now amend your ways and your doings, and obey the voice of the Lord your God; and the Lord will repent him of the evil that he hath pronounced against you.
Ezekiel 18:30
Therefore I will judge you, O house of Israel, every one according to his ways, saith the Lord God. Repent, and turn yourselves from all your transgressions; so iniquity shall not be your ruin.
Jonah 3:10
And God saw their works, that they turned from their evil way; and God repented of the evil, that he had said that he would do unto them; and he did it not.
Matthew 4:17
From that time Jesus began to preach, and to say, Repent: for the kingdom of heaven is at hand.
Repent, turn from your sins, and God will forgive you.Why do you not believe this was how sins were forgiven in the OT? No sacrifice nor offering was needed!
Even Jesus said this about repentance -
Luke 13:3
I tell you, Nay: but, except ye repent, ye shall all likewise perish.
He did not say, if I am not sacrificed on the cross, you shall perish.
Want to know what 'forgive' is in Hebrew? Perhaps you didn't know this. Among other things, it means to lift, bear, take away, and to carry.
Now you know. No blood, no sacrifice, no offering, no cross, no lamb, no priest, and no death. All it takes is for a person to repent, turn from their sins, and turn to God. Now that's mercy!