The Lamb of God was predicted in the Old Testament, from the very first lamb that was slain.
From the time in Genesis 3 when Adam and Eve first sinned, their sin needed to be atoned for.
The wages of sin is death. God, in his gracious love, chose an innocent animal to atone for their sin by shedding its blood.
The animal whose skin was used to cover their nakedness may even have been a lamb. God may even have sacrificed the animal in front of Adam and Eve.