The Beginning Of Offerings

In the beginning. The beginning of offerings do not much differ from love offerings or any other form of offering until the introduction of the Ecclesia and the Law. It was all done to bend the eye of God to harken for that given moment. Until the Mosaic time or the time of the Law and the prophets offerings were done voluntarily upon personal altars without an outline. It simply means it became a way to get God's attention before one can bend His ear to listen.
Yet one profound thing for any to watch and observe is that the first offering as the first seed was sown  also was done by God. Until the advent of Abraham; we do not hear God asking for specific things; but for God to do build and have a covenant with Abraham; we get to hear and know He progressively takes him about the longest round about one can go through or let us say in our common terms; Preparation.
He leaves Ur with his father and family; Abram and in the cause of time God does enable and prepare him to bring him to the more trained and experienced Abraham. It did not just take a title but the preparation too. It also goes for Jacob; after the patience and endurance of Laban's house, he was a ready man even to harken to his older brother Esau. It took both time and patience for Abraham to finally even hear the words; next year this time you will be having a son.
So, before the requests of God to Abraham, offering is not that much clarified. In fact in essence; we do not even know if the people withal Eden did begin to give offering when Adam and his family did join them or it was a means to maintain candidness or it came out with the exiled family from within Eden. We just do learn in the course of time; Cain did go to offer and his brother Abel tagged along; but to offer his first things.
So, apart from Abraham, we much on essence from the beginning just pick offering and first things from the exiled family and we do not even get to know the much about humanity outside the garden except that Cain did marry among the incumbents or occupants of Nod; then the espousing of others is not defined but rather the linage of the men child and their male offspring through the generations of Seth on.
The linage of both Abel and Cain are dropped along the way; a thing that means due to Cain being a vagabond and his sons be worse than him; Even as expressed in Lamech; his linage was not much to the praise but ruin of humanity so did the flood Noah did the unthinkable of the rest of humanity as it did to all the other branches of Adam. From the garden to the aftermath of the flood; only Noah emerges and his House.
A thing that brings in a new blessing; of course after Noah has offered to God his first things and when God is pleased He do bring in the New Blessing.