I don't know that it is impossible, so yes. But keep in mind that possible has two meanings. We use it to refer to things that we know could happen because they have happened before, but it can also be used to refer to things that actually are impossible, but we can't demonstrate it to be so. Gods fit that category. It may in fact be impossible for such a thing to exist, but if that's the case, we don't know it yet and may never know it.
Here's the problem from a pure reason perspective: Reality has either always existed, or something came into being from nothing and uncaused. I can't conceive of another possibility. It seems to me that one and only one of those must be true. Both possibilities are extremely counterintuitive. To have always existed means to have already passed through an infinite amount of time. That's not more palatable than something from nothing. I can't answer that question, and neither can anybody else, but it seems to me that whatever the answer is, it's "impossible." So, to look at only one of the options in isolation and reject it because it seems impossible to you is a logical error.
Here you are making that mistake - declaring one of the two possibilities impossible without simultaneously considering the equally counterintuitive alternative. I cannot and need not explain how that could happen. If you claim it can't, then it's you that has some 'splainin' to do. How do you know that that can't happen? Because you've never seen it happen?
I think you're using your private definition of universe here, but no matter. But regarding explaining, maybe you should explain how something can already have existed for an infinite amount of time (no beginning). Reality having a first moment and having no first moment are each counterintuitive, each seemingly impossible. Pick one if you must, but it'll be a guess. I prefer to remain agnostic. I don't know. Nobody does.
This argument has just been rebutted, and I'd say successfully. If you disagree, I await your counter-rebuttal - your explanation for why what I wrote here is incorrect in your opinion. Please not that I am not asking you what you believe, but to tell me why you consider me wrong if you do.
That was in response to, "the value of that knowledge [whether the universe or multiverse collectively is conscious] would be about zero even if we had an answer." No, I don't see all human beings as intellectually equal, but I still conclude that the answer to that is not useful information. If we are pieces of a conscious organism, then we have the same status as the pieces of ourselves. Imagine that our constituent neutrons, protons, and electrons were conscious. Would knowing that they are part of a larger, conscious whole be useful knowledge to them?