Hi Stan,
Good question with a simple answer - the Early Church Fathers (as a whole) did not confirm Paul as the author of Hebrews (some did, some didn't).
The Early Church Fathers was a mixed bag. Eusebius did note that some (contemporary to Eusebius) rejected Pauline arthurship and that the church of Rome disputed Hebrews because they rejected it was authored by Paul. Tertullian viewed Barnabas as the author, Hippoltyus attributed it to Clement of Rome. Origen noted that some believed Clement or Luke to be the authors. Giaus of Rome did not believe it was authored by Paul.
So to answer your question, long before 300 AD the authorship of Hebrews was questioned. What settled it for most is tradition, and that most likely a result of Augustine, not the Early Church Fathers (obviously).
But the reason I reject Pauline authorship is simple. The book does not read like it was written by Paul. For one, I think it reasonable to expect Paul to have written to a Jewish audience turning back towards the Jewish religion in Hebrew. Even the Greek used is not the styling we would expect of Paul. BUT many have suggested (to include Eusebius) that this can be accounted for by Paul dictating to Luke. And that is a fair suggestion.
There are other problems. The author of Hebrews does not seem to be an apostle (just by the writing). The author speaks of salvation being confirmed to him (and others) through one or more of the Disciples (Heb. 2). But this was not the case with Paul. The pattern of speech does not even come close to Pauline. The theology is similar, as would be expected of any of the suggested authors, but not exactly what we would expect from Paul either.
So my answer is that I do not know who wrote the letter. The Early Church Father's did not know (they had many ideas). So how can we say that we know?
More importantly, why do you believe that Paul wrote Hebrews?
Caldwell, I am under no illusion that the Church Fathers were Divinely inspired. And you are the first person I have encountered, who is aware that the attack against the "The Epistle of Paul to the Hebrews", was the Church at Rome!! They not only denied the authorship, but the 'Canonicity' of Paul's Epistle to the Hebrews. No big deal. Nothing good comes out of Rome. Rome was already the seat of political corruption and apostasy.
Caldwell >> "Tertullian viewed Barnabas as the author, Hippoltyus attributed it to Clement of Rome. Origen noted that some believed Clement or Luke to be the authors. Giaus of Rome did not believe it was authored by Paul."
I am most disappointed to hear that Tertullian viewed Barnabas as the author. :-( I have revered Tertullian as perhaps one of the most orthodox of the Church Fathers, corresponding in most ways to the beliefs of the church of today.
Familiar with the works of Barnabas, it is clear to me why his Epistle was not included within in the Canon of Scripture. He added a whole bunch of law to the Bible that were never included in Scripture. He added a whole bunch of repressive laws to Scripture I suppose we could designate him at the unscriptural current unScriptural anti-abortion movement: "Thou shalt not destroy the conception of thy womb, nor kill it after it has been born. (9:15?)
I have no problem in accepting the authorship of Paul's "The Epistle of Paul to the Hebrews", the way it was presented in the Hebrew, but deleted by those who translated it into the Greek. A title still retained in the KJV.
What I believe, although soundly supported by Atanasius, Eusibius, Irenaeus, et al, is the promise of the Holy Spirit to lead us into all truth.