I found this regarding the Hebrew, and I assume it is probably true: "The Hebrew equivalent of 'hamartia' is 'chata'."
Now, I very much would predict that if you study it, the fullness of the concept of "amartia" is probably Hebrew at its basic root, and "amartia" was probably the Greek word selected to carry the concept, probably by the translators of the Septuagint Old Testament, long before the birth of Christ.
A concern for missing the mark of perfection with relation to God and morals doesn't strike me as a pagan Greek philosophical concern, but I may be wrong.
Orthodoxy has been described as Hebrew concepts conveyed and expanded with the Greek language -- probably the most powerful language in the world for conveying Christian theology. Part of Christ's coming 2000 years ago "in the fullness of time" was that Greek at that point was the common language of the Roman empire. The language played a huge role in the flowering of Christianity, both in the sense of missionary work, but also in the ability to express with precision the faith that Christ had given to his apostles.