There are indeed rare, extraordinary phenomena, whether they be recovery from near impossible medical emergencies or survival without injury from natural disasters. There has even been drastic character transformation in formally malicious people who converted to Christianity. Consider the notorious example of the Apostle Paul. It would be much more reasonable to attribute such to supernatural intervention than to mere chance.
We should not make the hasty generalization of dismissing authentic miracles alongside the counterfeits. The authentic experiences serve as evidences for God being very much alive throughout His creation. The real issue is that we lack faith in Him. That is a tendency of our fallen nature.
Empirical evidence is not the only form of available evidence. We also have experiential knowledge and eyewitness testimony. One need not assume without proof that the New Testament writings are historically fraudulent, especially when it has so much manuscript evidence favoring its veracity.
Scientific experiments tell us how nature regularly operates under certain conditions, not that miracles are an impossibility. Thus, there are both natural and supernatural explanations. It is because of our scientific knowledge that we can discern whether an occurrence is a miracle. Miracles do not contradict natural laws, but rather transcend them.
Furthermore, it is a highly unscientific to assume that God does not exist because such a colossal argument requires that one obtain infinite knowledge about everything. This cannot be done by beings who are finite by design. He is beyond the limited scope of nature. A test-tube will never be capable of coherently explaining away the fullness of reality.
If the God of the Bible does exist (which we maintain that He does), then the case is closed. He can indeed work miracles, and does. Miracles are not impossible when viewed from this framework.
Even if there were no supreme deity governing the universe, atheism would still have no reason to exist or proclaim itself to be true.
Atheism is inherently self-contradictory because it appeals to universal laws which cannot exist if everything arose by blind, mindless chance. The concept of moral truths would be no different than our personal appetites. Even our own existence could not be objectively true.
Atheists express circularity in their denials of the miraculous: "Miracles do not happen because they do not exist; miracles do not exist because they do not happen."