I think of existence as a concept defined within our universe. It is not well-defined for anything outside of it. Something can't exist if there isn't a universe to contain it. Hence the universe came first. Or at least simultaneously – otherwise it might suffer existential pains.
However, I do think you might have an interesting point. In more abstract terms, the timeline of the universe is the chain of cause-and-effects that lead to what we presently observe. Events following the Big Bang are the cause-and-effects that conform to the known laws of physics, with minor fluctuations around the big bang itself, or so I'm told. This also makes them easy for us to study and understand.
However, you could go beyond that. For example, you could look for a reason why the laws of physics are as they are. Two candidates are random chance and the anthropic principle, which is just random chance with observation bias. If you do come up with a third reason, it could be a "cause" of the laws of physics and therefore be "before" the Big Bang (if you replaced time with causes and effects). Unfortunately, such reason would probably be impossible to falsify, difficult to put in terms we understand, and would barely resemble any real temporal relationships. But you could call it "The Big Would-Bang".
