What is the evidence for Paul writing the Book of Hebrews?
Firstly, let’s observe that this book does not begin as a typical NT epistle. While the ending is like a regular epistle, the beginning differs in that there is not the usual greeting with names of the writer and the people to whom it is addressed. Throughout the epistle it seems to be addressed to a Christian community, but it is not named.
This epistle was known to Clement of Rome before the end of the first century (ca. AD 96) in a letter he wrote to the Corinthian church from the Roman church. See 1 Clement 36:1-5. Some of the language of Hebrews is interwoven in these verses from 1 Clement.
As for the author of Hebrews, I believe the best answer is that we do not know who wrote it. Clement of Rome gives not the slightest indication who the author was. There was an Alexandrian belief of Christianity from the East in the 4th century that Paul was the author. This seems to have influenced the view that people espouse that Paul was the author. Clement of Alexandria in Hypotyposes [quoted by early historian Eusebius in Ecclesiastical History 6.14.2] claimed that Paul wrote it in the Hebrew language and it was translated by Luke and then released for the Greeks to read.
We do have another early reference to the authorship of Hebrews from Tertullian (On Modesty, ch 20). He claimed that it was written by Barnabas. Look up the writings of The Muratorian Canon, Irenaeus, Hippolytus, and Gaius of Rome, as none of these regarded Paul as the author of Hebrews. The main early influences in pointing to Paul as the author of Hebrews came from Jerome (Epistle 129) and Augustine (On Merit and the Forgiveness of Sins, and the Baptism of Infants 1. ch 50). Augustine supported the Eastern church’s view and the placing of the Book of Hebrews in the canon of the NT. Jerome said that there were 3 views of the authorship of the Book of Hebrews when he wrote about AD 414. The Epistle was written by Paul, Barnabas or Clement, according to him.
From the Synod of Hippo in 393 and the Third Synod of Carthage in 397, we have the statement, “Of Paul the apostle, thirteen epistles; of the same to the Hebrews, one”. At the Synod of Carthage in AD 419, we have affirmed “fourteen epistles” assumed to be ascribed to Paul. From this time forward, Hebrews was said to be from the pen of Paul in the Western church, but Clement of Rome or Luke as a translator or editor of the epistle were ascribed authors. Thomas Aquinas (AD 1225-1274) in his Preface to the Epistle of the Hebrews wrote: “Luke, who was an excellent advocated, translated it [Book of Hebrews] from Hebrew into that elegant Greek” (quoted in F. F. Bruce 1964. The Epistle to the Hebrews, Eerdmans, p. xxxix).
Therefore, assigning the authorship of Paul to the Book of Hebrews is questionable in my view. For me, the best view is that the author is unknown, but that the Book of Hebrews was an important book in the canon of Scripture from the early years of the Christian Church.