To believe on Jesus is more than mere assent to the fact. Jesus is the true sacrifice in which the animals are a type.
In order to have forgiveness one had to see their sin/transgression of the law and in sorry for sin bring a perfect lamb or sacrifice to the sanctuary and confess their sins on the head of the lamb and then take the life of the lamb as a symbol that their sin cost innocent blood. then out of their realisation and sorrow for sin and the cost of that sin they would determine to no longer commit known sin.
Otherwise known as repentance or turning form sin and turning to God.