In what sense is God's provision of animal sacrifice for forgiveness of sins an expression of his mercy?
God used the sacrificial system of sacrificing various animals to teach the Jews lessons of sin, holiness, confession, forgiveness, sin's costliness, and sin's horror. God, in his mercy, allowed these sacrifices to purge their sins.
Were animal sacrifices actually adequate to atone for human sin?
No - they were not adequate. It was not possible that the blood of bulls and goats, nor the blood of any other animal, take away our sins.