Some people claim that China's population is half of what the officials claim.
“entire countries” of population spans a range from single-digit hundreds to over a billion, so this could describe anything from an imperceptible error to an enormous one in China’s case.
I'm sure the various high-end intelligence agencies have a much better view on this than the public does. All kinds of ways of cross-checking the numbers, all by doing things they'll be doing in their normal course of events.
A normal person could probably do a decent job with an AI that isn't too biased in the direction of "trust gov numbers above all else" and tracking down and correlating some statistics too obscure and too difficult to fake. (Example: Using statistical population sampling methodology on some popular internet service or something.) The main problem there being literally no matter what they do and how careful they are, they'd never be able to convince anyone of their numbers.
The problem with trying to measure this as a normal person is that you don't have enough access to different types of measurements to build good models of sample bias and selection artifacts.
Some people claim that the Earth is flat. I’m rather more inclined to believe China’s official statistics than what ‘some people’ on the internet have to say.
With modern technology/knowledge, we have a lot of high-density calories lying around, in the form of grains, potatoes, oils, etc.
It might be possible to get a rough picture tracking the perishables that are often animal products but poor countries don't use a lot of it because, well, they are poor. So it makes everything very complicated.