Why does God make garments of skin at Gen 3:21? Moreover, why is this said to be the first sacrifice?

The garments serve to cover Adam and Eve’s nakedness, which symbolizes their sin. But why a “sacrifice”? First of all, it seems unlikely that God would have made “coats of skins” without having slaughtered some animals for those skins. Moreover, the garments were made for Adam and Eve, both for their benefit and to cover what it would (when more people are on earth) it would be a shame to be seen. Finally, as a commentator puts it, God is covering their sin, and saving them from immediate death, whether from exposure or through execution—and doing so by taking another life, so that there is a life for a life. This is not unlike the sacrifice of Jesus as a covering for our sins. The latter comparison seems even more apt when one considers that Adam and Eve had attempted to cover their “sins” with the fig leaves, and yet that covering, made through their own efforts, was deemed totally inadequate by God. Of course, there is no reason to think that there was anything like a sacrifice in the sense of ritual ceremony that was done in the making of the garments. But that does not undermine the suggestion that they did serve as sacrifices. The basic notion, found in Lev 17:11, arguably applies here: “For the life of the flesh is in the blood: and I have given it to you upon the altar to make an atonement for your souls: for it is the blood that maketh an atonement for the soul.”