It would appear from the gospel stories that God can and does forgive without sacrifice.
Rhoads, Dewey and Michie say in Mark as Story, page 113, Mark's Gospel portrays Jesus already pardoning sin during his life and authorising others to do the same. His death is not needed to make forgiveness possible, so Mark does not portray Jesus' death as a sacrifice for sin. The crucifixion as atonement for sins comes in later traditions.
Partial transcript from page 113 of Mark as Story
The meaning of Jesus' crucifixion The
The significance of-Jesus'death became a central concern of later Christian theology. The theological significance of the death is not, however, Mark's primary concern. Although the Gospel does suggest some meanings for Jesus' death, as we shall see below, what is central for Mark is that Jesus was executed and raised.
. . .
Therefore the modern reader needs to be cautious not to read into Mark theological meanings that later came to be associated with Jesus'death. To begin with, Mark does not portray Jesus'death as a sacrifice for sin. Mark portrays Jesus already pardoning sin during his life and authorizing others to do the same. His death is not needed to make forgiveness possible.
[my emphasis]