How do you have time without space-time? The big bang is actually not the exact start of the universe. It's pretty close, but not quite. It is the expansion of the universe. Before that it's in a very dense high energy state, but it does exist. It explains how it went from this state to the current state, but not how it came into existence at all.
I don't think it's believed to have sat in this dense high energy state for infinite time before the big bang, so it must have come into existence, not just existed forever. If that's the case that means space-time came into existence. You can't have time without space-time, so there is no time before it exists. At some point space-time exists, and as such there is no before, since there is not time.
It seems odd to consider. How do things happen without space-time? We can't really think about this concept, because we're space-time beings. It doesn't even make sense to consider. However, having an intelligence start things doesn't help. It only then begs the question where they came from. Surely the universe just starting is more likely than an intelligence appearing for some reason, then it deciding to start the universe. That's a vastly more complex set of circumstances.