A child through their formative years will likely be influenced by their parents and take their word for it until they get to the age where they will make their own choices.
But generally, I would accept your premise that there are 3 possible choices: acceptance, rejection or uncertainty. And uncertainty would be the default condition. However, this would be case for almost any topic: politics, sports, careers. Uncertainty is usually followed by either more uncertainty or a decision.
"Burden of Proof" and "deviants" are interesting choices of words. I think if anyone is attempting to come to an honest, impartial decision on the existence of God, using language like this will lead them to the wrong conclusion by "default".
From my point of view, a Christian believer, God has given everyone a choice. Every one must make a decision reviewing what they know and coming to a conclusion. Even indecision is still a choice. There are plenty of reasons to believe if you start from an impartial position.
For me, no one had to convince me of my beliefs. There was wasn't a burden of proof placed on anyone. I started with several basic assumptions that eventually led to a logical conclusion: belief in the existence of God and Christianity as the avenue to Him.
The first assumption was to recognize that if God was real, He doesn't necessarily think like us. In the same way if we met space aliens, they probably wouldn't think like us. The same would be true of the Being described by the Bible. A Spirit Being outside of space time, who created everything, with infinite power and understanding. So simply dismissing God because something doesn't appear to make sense to us should not happen. But does that mean we accept everything? Not at all...
The second assumption was that if something didn't make sense, it still had to be rational. There cannot be obvious contradictions without resolutions. In my studies over the years, Christianity continues to be logically consistent. The framework that it is based on is solid and even the detail holds up. Through process lasting 6-7 years, I moved from being agnostic to being a firm believer. That was 10 years ago.
Really, there isn't a "burden of proof". There is decision and a decision making process. If Christianity is to be believed, there are very serious consequences for not believing. I'd wouldn't recommend resting on being an agnostic. Searching for the answer yourself, apart from what others believe is the best route.
Finally, the Christian view of God is one of a personal Being, meaning He does hear when you talk to Him. One thing that He will ALWAYS hear, whether you are a believer or not, is a desire to know Him and know the truth about Him. Remember, He doesn't think like us and He isn't obligated to do anything for anyone. But being real with Him goes a long way. Give it a try...