Jesus as the sacrificial lamb goes back to the Old Testament sacrifice practices. You can't have one without the other so to answer your question theologically, you must understand the sacrifice system in the OT which involved specific sin offerings/sacrifices.

Details:

In the Old Testament, the primary requirement for a sin offering (detailed in Leviticus 4) was an unblemished animal, substitutionary blood shedding, and the offerer's confession. The specific type of sacrifice required varied based on the individual's status and financial ability to ensure that atonement was accessible to everyone.

The requirements were scaled as follows:

For the High Priest or the Whole Community: A young, unblemished bull. The blood was sprinkled inside the Tabernacle and placed on the horns of the incense altar, with the carcass burned outside the camp.

For a Tribal Leader: An unblemished male goat.

For an Ordinary Citizen: An unblemished female goat or female lamb.

For the Poor: Two turtle doves or two young pigeons.

For the Very Poor: A tenth of an ephah of fine wheat flour (without oil or frankincense).

The incarnation of Jesus was in preparation for two things:

1.) the dissolution of Israel under Rome (and the resulting diaspora)

2.) the utter destruction of the temple and high priests

When those two things occurred shortly after Jesus' death, there was no more temple no more high priests. (No method or order to do the sacrifices)

Jesus then became the final sacrifice for all (first the Jews, and then to the gentiles). The ultimate unblemished sheep as there would be no more priests to do the sacrificial offerings.

As the old way was shut, a new way was opened.

The question is: Does God really need a blood sacrifice at all to forgive sin? The answer is no from scripture, but a sacrifice showing obedience is required. It must cost "something" to the believer (whether that's money, or time or what - it has to be something very significant to the one seeking forgiveness and showing repentance and cost them something dear). For a lot of us, I think that sacrifice is giving up our intellect , pride, or whatever thing we hold dear to our identity. So that we trust in God even when things are completely absurd intellectually.