You can't do it scientifically (read until the end) or everyone would know from the beginning. You cannot possibly keep this a secret if a high school experiment will disprove everything people think they know about the world. Also, if more advanced scientific equipment is needed, well, such a totalitarian government wouldn't fund it. I'm worried about the integrity of your world here, so let's save it.
So he needs to do what nobody else has done so far and was in the position to be lucky: be lucky and overhear/see/notice something is up. Some people have to know and people make mistakes. How this happens is story-based, but unless this is for a kids book getting that information from someone else is an easy way to keep your world intact. There must be food deliveries, I would start there.
So, you asked about "scientific" specifically, so here I go: Alcohol. The best way to get that information it is alcohol. A person under the influence of alcohol is more likely to tell you stuff. If you don't like that idea: a blow to the head, any other drug, lack of sleep - there are a lot of options here.