How can the universe exist without us? Take a practical example: (let's assume that Earthly beings are truly alone in the Universe)
We are all here. We observe the Universe. To our current knowledge - it exists. Period.
Humans disappear.
Only sentient and conscious beings (bears, birds, whales, tapeworms, ETC) exist on earth.
They are not aware of the concept of the Universe, or even what they mean on Earth for that matter. But they still exist, do they not? And the Universe they live in still exists, does it not? Just because they have a (very) tiny fraction of understanding of life and its complexities compared to what now-extinct humans had, this doesn't mean they are not contributing the Universe's functions.
Every animal dies. Except one Blue Jay.
The Blue Jay looks around and suddenly gains 100X the intelligence that humans once had. He thinks he knows (nearly) everything that could be known about the Universe. But he has no one to share it with. Does the universe exist still? Yes, of course, it does. Our Blue Jay exists in it. He thinks. But also breathes. And flies. And eats. And poops. DOES.
The Blue Jay dies.
Is the Universe still there as the bird dies? What about the very second its body ceases life functions. Does the Universe simply fade away? No, it exists. But nothing sentient or conscious is alive OR aware of it.
There is nothing to say that one rock on some distant planet in some distant galaxy on the other end of the Universe exists any less than your brother Timothy does. It just doesn't think, breath, fly, eat, or poop. But it DOES. Does what? Exist.
It is careless and fallacious to think that that one aspect of existence (consciousness) is the sole factor for justifying the grander, MUCH larger process that makes that very aspect (as well as many others) EXIST in the first place. In fact, it's so careless that it's a personal insult. (Not to me, but to the Universe)