Well, I for some years now, have missunderstood Hebrews 2:3 too.
". . . at the beginning began to be spoken by the Lord, . . ."
Paul excluded himself here.
If one reads Heb 2:3 carefully.
Heb 2:3 How shall we escape, if we neglect so great salvation; which at the first began to be spoken by the Lord, and was confirmed unto us by them that heard him;
Putting faces to the pronouns will help greatly in the above verse.
The writer is not claiming to have been there when Jesus spoke of this great salvation, which was probably his words to the 11 apostles and the 70 elders post resurrection. He is claiming to be among the Hebrews who had his words confirmed to them by signs and wonders and divers miracles and gifts of the Holy Ghost.
He is probably not referring to a one time event of confirmation by these signs but a continual display of these signs over maybe a period of about seven years until the death of Stephan in Acts 7 when the rulers during that generation in Jerusalem rejected Jesus Christ for themselves and the nation finally and forever and killed the messenger. It was at this time that the gospel of Christ began to exceed Jewish bounds, going to Samaria. After this, the door of faith was opened to the gentiles by Peter, who had been given the keys to the kingdom of God in Matthew 16. Paul had been saved in chapter 9 in a miraculous conversion between the Samaritan (chapter 8) and the gentiles salvation (chapter 10).
According to Paul, who has stated his credentials in the Jewish religion and as a Jew, there was no one on the planet as qualified to write Hebrews and make the application to the person of Jesus Christ than he. He is the one man who had seen the risen Lord 3 times and had been taught by him and been given the revelation of the "mystery of Christ," the church in this age and would have been able to make the spiritual applications that affected the Hebrews better than any man.
Peter, writing to the strangers scattered throughout a stated 5 provinces of Asia Minor (1 Pe 1:1-2) made this statement about Paul and his writing to them.
2Pe 3:15 And account that the longsuffering of our Lord is salvation; even as our beloved brother Paul also according to the wisdom given unto him
hath written unto you;
16 As also in all his epistles, speaking in them of these things; in which are some things hard to be understood, which they that are unlearned and unstable wrest, as they do also the other scriptures, unto their own destruction.
These are Hebrews, though displaced from their own land and called strangers, They are called in Ga 2 the concision and are those whom the 12 apostles are called to minister to. The same warning of Hebrews is suggested by Peter in his letter.
Another indication that Paul is the author of Hebrews is the salutation. All his epistles end like Hebrews ends.
He 13:22 And I beseech you, brethren, suffer the word of exhortation: for I have written a letter unto you in few words.
23 Know ye that our brother Timothy is set at liberty; with whom, if he come shortly, I will see you.
24 Salute all them that have the rule over you, and all the saints. They of Italy salute you.
25 Grace be with you all. Amen.
My vote is Paul as the author of Hebrews.