Why does the Universe exist? There are two questions here.
First, why is there a Universe at all? It might have been true
that nothing ever existed: no living beings, no stars, no atoms,
not even space or time. When we think about this possibility,
it can seem astonishing that anything exists. Second, why does
this Universe exist? Things might have been, in countless
ways, different. So why is the Universe as it is?
The questions are wrong. Reality is what it is and cannot be anything else. The reality is, there is the universe. What is, is, and couldn't be something else. If you believe it could be something else, you must explain how. It implies something caused reality that could have failed to cause reality or could have caused to be something else. Since reality includes every thing there is, even an imaginary cause, it includes what that cause actually did, and what it did was cause the universe there is.