No doubt, the Hittites existed and were a power. I don’t see how this causes problems for Christian theology, however.
Indeed, the existence of the Hittites have no bearing on Christian theology. While it's been many years since I've heard it, some claim that since the Bible mentions Hittites but the Hittites (at that time) aren't mentioned in any other reference, then the Bible must be wrong.
History once again proves the Bible correct.