I think it's not so much a 'direct grab' at being but more a provisional, circumspectional understanding, a formal indication. Indeed, by the mid-thirties, Heidegger didn't think you could get at being solely through Dasein. Society and culture, structures and practices, which imbue themselves in Dasein, also need to be accounted for.
Nevertheless, with that said, I wanted to just draw attention to the manner in which I have gone about reading B&T and which may help a little to some of the other readers. I don't know....
The provisional claim, the one being worked over in the entire text is that being is not a substance of any kind, it is not a form, a god, a substance with predicates, or what have you, but merely "that on the basis of which entities are already understood..." (p25:6).
This means that whatever being is, however some-thing, whatever that some-thing be, makes sense to you, it has to do with your understanding, intelligibility, a comprehension of some kind. Now, this is radical. The entire tradition has pretty much said that being is the most general property, universal, indefinable and self-evident, but if you start framing being as something which is understood by you and your kind, you're beginning to undercut some of those notions.
If you stop to pause at page 25, already little questions should spark: Understood by what? When? How? Under what circumstances? And you can appreciate that the given answer, the ones you give youself right here, may not necessarily be universal, indefinable, a general property and self-evident.
Indeed, playing along with Heidegger just at this page, without any need to read on, what does it mean for something to be understood? If something, for me, is understood, then as I reflect on that which is understood, I'm already having to draw on a bewildering frame of other features and characteristics. The pen, to be understood, needs to draw itself or refer to other things like ink, plastic, ball-points, paper, which again, refer to other things, like wood, oil, which in turn refer to other things, and just for the sake of argument, point to implicit understandings of language and writing, given social practices, ways of behaviour and activities in given historical times, education, and so on. The being of the pen, as something understood by me as a pen, even at this most basic level, once reflected upon has a most complex way of being.
Okay, so we read on a little more and we get to "Being arises from the average understanding of being in which we always operate and which...belongs to the essential constitution of Dasein itself." (p28.8).
Being belongs to Dasein! Our understanding of being arises from us. And what of this 'average understanding' what does that mean? At this point, I didn't read on. I put the book down and went for a walk, I went to college and to work, strolled the park, watched the children and the families, went to a bar and had a coffee. Certainly, I saw folk dealing with things. They were walking the streets, going in and out of door ways, picking up pens and bags, exchanging money for goods, picking up forks and knives in a general manner, dressed in a way, talking in another, going about their lives coping and struggling, and if I asked a child or an adult in class what theoretical concepts, hypothesis, theories, grammars they were drawing upon as they went about their everyday life, they, like me, couldn't give an answer.
They were just doing their thing, skillfully doing things without, in many cases, any deep reflection and certainly not drawing upon complex theories as they went about their daily lives. Most folk I encountered had this practical comportment towards the world of being. They, like me, knew-how to go about, and generally knew what they had to do.
And this led me to think what is the structure of that kind of fundamental understanding, what of the world these fellows move about in, what of their encountering with others, and so on. I went back to the book and read on.
In this manner, reading, reflecting, re-reading, reflecting, will mean that B&T will take years to read, but there's really no hurry. If the language throws you, don't worry. Just reflect on what you do grasp and even that will be something very significant and life rewarding.