I think the problem with this question is the use of the word “why.”
Yes, I think with the question “Why does anything exist at all?”, the technique would not go “Why do I think anything exists at all?”, but rather: “Why do I think there is a reason for anything to exist at all?”
Yes, I think with the question “Why does anything exist at all?”, the technique would not go “Why do I think anything exists at all?”, but rather: “Why do I think there is a reason for anything to exist at all?”