That's a tough and interesting question, and I'll admit it's hard due to the lack of empirical/testable claims made by Christianity. Even if some guy claimed to be the second coming of Jesus, and performed convincingly supernatural miracles, I don't think this alone would convince me of Christianity. The reason for this being that this event could be caused by Christianity, but it could have other explanation. Maybe no God exists, only Satan does, and this man is the son of Satan who wants to trick us into worshiping him. Or perhaps this man is just some guy who happened to be born with supernatural powers for no reason and he wants to convince us he's the son of God for laughs. These scenarios might seem ridiculous, but I don't see why they should cohere with my preconceived notions any less than Christianity does. The only 'advantage' Christianity has is that a lot of people believe it, but that has little bearing on the truth value of Christianity. As for your question. Perhaps one could, through pure reason prove the existence of a God which is omnipotent, omniscient, and omnibenevolent. Being omnibenevolent is important, since if the God isn't known to be all-good, then it might be an evil deity forcing me to believe it is the Christian God. Once this all-good God is proven to exist, the task is then reduced to proving that this God is, in fact, the Christian God. Maybe you could point to an undeniable example of divine intervention, one which is consistent only with the God of Christianity. If you could execute these two tasks with reasonable rigor, I think you'd have a strong argument in favor of Christianity.