Here in Hebrews 13:12-16, Paul is outlining the proper order of sacrifice in our life, which is interesting in that it is slightly different from the initial order given in Leviticus of the burnt, grain, peace, sin, and trespass offerings. Why is that? Well, the order here in Hebrews 13 is the same found in Leviticus 9, which records the first observance of the Aaronic priesthood.
In both Leviticus 9 and in Hebrews 13:12, we see that first comes God's sacrifice. The sin and trespass offering has to come first to open a door and enable our relationship with God. We could never approach God as a whole burnt offering in complete devotion to God until Jesus Christ's sin offering suffered outside the gate, opened the door to our relationship with God. That had to come first.