Foreshadowing. God loves a good story, played out in many acts.
Or, if you want to get progressive about it, God was slowly, through the ages, weaning His people away from child sacrifice, to animal sacrifice, to the One Perfect Sacrifice, that can cure all.
For that matter, why not have Jesus born at the time of Moses or Isaiah instead of when he was? He could have been executed by the Egyptians or Assyrians instead of the Romans. Why that time?
Dunno. God has to have some reason, don't ya think? For one, the time was right in the development of the people.
SD
Maimonides speculated that the progression in the Hebrew scriptures was away from animal sacrifice; that it was originally permitted as an accommodation to the wishes of the Israelites, but was gradually restricted over time.