If fires didn't burn orphans, it may be technically true that science couldn't prove it was caused by a God, but that's because science can't prove anything. Science certainly could rule out other explanations to the extent that a godlike being is pretty much the only reasonable possibility left. Science could discover that fires not burning orphans seemed to be a fundamental law of the universe that can't be explained in terms of other laws. And a fundamental law of the universe that operates in terms of complicated human conceptual categories like "orphan" is a miracle.

You seem to think that science could never prove this is a miracle because science would just keep coming up with other theories (that would eventually be disproven). If that was actually true, no scientist would be able to conclude that anything is a fundamental law of the universe at all, whether miraculous or non-miraculous, since the scientist would keep coming up with theories that explain the law in terms of something else. In fact, at some point the scientist will run out of likely theories and will only be able to come up with theories so unlikely that "this is not based on some other law" is more reasonable.