If you think Paul wrote Hebrews, you’re in good company (see, e.g., here). One problem with this conclusion, however, is that what Paul says in Galatians 1:11–12 seems to contradict what Paul says in Hebrews 2:3, presuming Paul wrote Hebrews 2:3. That is, in Galatians 1:11–12 Paul emphatically states that he received his gospel directly from Jesus, whereas Hebrews 2:3 seems to imply that its author could not say the same thing. “This salvation [i.e., gospel]... was first announced by the Lord [and] was confirmed to us by those who heard him.”
It’s possible that the two texts are compatible, of course, since Hebrews 2:3 doesn’t clearly deny that its author received his gospel—“this salvation”—from Jesus himself. Perhaps it only suggests that an initial reception was later confirmed by eyewitness testimony (“those who heard [Jesus]”).
This sort of reading, however, is unlikely. The author talks about the gospel being “confirmed” in Hebrews 2:3 not to distinguish between its initial reception and its later apostolic confirmation. Rather, the author talks about the gospel being “confirmed” because he wants his doubting audience to know that God has really spoken a new word, a “great salvation”—a word that is even more “binding” than his previous word given through angels (Hebrews 2:2; i.e., the Law). After all this new word was spoken “by the Lord,” which is to say, by the one now seated at God’s right hand (see 1:5–14; see, similarly, Phil 2:9–11). Surely he is trustworthy! (Otherwise, he’d never have been given such honor.) And, moreover, the reality of this new word had been confirmed throughout the Roman empire, including among the author’s audience (“to us”), by those who’d seen and heard the now-exalted Lord. The author is certain his audience will remember all this, especially since the evangelists’ message had been accompanied—and further confirmed—by “signs, wonders and various miracles, and by gifts of the Holy Spirit” (Heb 2:4). Surely they’d not forgotten such a memorable event (see, similarly, Galatians 3:2, 5)!
In short, Hebrews 2:3 talks about the author and his audience’s initial evangelization. Their community was a result of the apostolic mission. And, as such, Hebrews 2:3 contradicts what Paul says in Galatians 1:11–12 and, thus, suggests that Paul did not write Hebrews.