Purification Offering for the Anointed Priest
Hebrews does not ask us to guess whether the outside-camp detail points to Jesus—it tells us to notice that pattern. That explicit inspired connection is stronger than dozens of imaginative ritual-detail parallels.
Where this fits in the story: Exodus 29:10–14 — very strong covenant/ritual background. Priest-consecration already includes a bull purification/sin offering and burning its remains outside the camp.
Where Scripture takes it next: Hebrews 13:11–13 — certain/explicit inspired comparison. Hebrews recalls sin-offering bodies whose blood is brought into the sanctuary and whose bodies are burned outside the camp, then compares Jesus suffering outside the gate.