What's the difference?
If you have a car wreck tonight, was it God's will, or an accident? If you believe God has His hands in everything, then it was Gods will. If you belive otherwise, then it was just an accident. In either case, it happened, and the outcome is the same.
Same with Neaderthals. Whether you believe God did it or it was just an accident, it happened. The outcome was the same. There's no way to tell the difference between the two objectively. The only way to "know" is by your personal faith, which can be anything you want it to be, and so doesn't clear up the question.