Theoretically, God could have intervened at any point throughout history. In fact, God could have created the entire universe 1 month ago. He could have implanted in every individual's mind false memories and created nature with the appearance of age. You can do this at any point in history, right up until the very last instant.
There are a couple problems with that type of idea. Creationism lacks the empirical rigor necessary for scientific hypotheses. There's no way to possibly check, verify, or falsify it. In short, it's not at all scientific. Second, the evidence that we have overwhelmingly points toward evolution of life over billions of years. Because the evidence points toward a slow descent of life, we have to reject creationism on theological grounds.