A couple major things on this one. First, we’re not sure on the author. Could be Paul, but Hebrews man argues a bit differently than Paul (although he’s verbose and knows his OT, so I ain’t saying it ain’t Paul either.) Other thoughts are guys like Barnabas or some such similar dude or potentially even Priscilla (of Priscilla and Aquila fame).
Although generally titled as a letter to the Hebrews, a letter usually has a greeting with the name of the author, which would’ve cleared up the matter. That said, like a letter, there is exhortation and encouragement towards the end as well as parting thoughts that end in a personal appeal, greetings from other folks, and the extension of grace. It’s a weird combination.
For timing, it was most likely written prior to AD 70 given the references to the sacrificial system with no reference to the fall of the Temple (if you’re trying to dissuade someone from going back to a no longer needed atonement system, mentioning that you can’t even do it anymore because the Temple is destroyed would seem like a must-use argument. The absence of it is telling.) So, think 60-70 AD for context.