I provided the very scripture that used the word "offering." But here it is again.
"And the LORD looked with favor on Abel and his offering, but He had no regard for Cain and his offering"
"By faith Abel offered God
a better sacrifice than Cain did. By faith he was commended as righteous when God gave approval to his gifts. And by faith he still speaks, even though he is dead." - Heb.11:4
Do see it now? Paul, is referring to Cain and Abel and notice the word that he uses is "sacrifice." But even if Paul had not described what the offerings were, it is because of the teaching of shed blood.
God accept Abel's sacrifice because it had to do with shed blood. Cain's sacrifice was rejected because it did not having have anything to do with the shedding of blood. Cain's sacrifice represents our own works. Below is the definition of the word
HELPS Word-studies
2378 thysía – properly, an
offering (
sacrifice); an official sacrifice
prescribed by God; hence an offering
the Lord accepts because offered on His terms.
2378 /thysía ("sacrifice")
refers to various forms of OT blood sacrifices ("types") – all awaiting their
fulfillment in their
antitype, Jesus Christ (Heb 10:5-12).
I hope that this is beneficial
Blessings!