I, uh, happen to be an expert in censuses.

The US of course tries to get everyone to respond, and sends people out to follow up with people who don't respond, such as this sovereign citizen in the original post. (The picture is of the 2020 Census envelope and as such is ~4 years old, by the way.)

Some European countries do an administrative records census, wherein they know who is in the country based on passport control, birth and death records, and so on. These censuses have the (admitted) flaw that someone who is in the country illegally would almost certainly not be counted, but on the flip side they are MUCH cheaper and faster than the US-style census. It's basically just running an SQL query on the database.

Other countries do a mix of the two. Even the US uses administrative records sometimes, if good data is available, and they can't get a response another way.

The US's situation is more complex than many countries, because driver's licenses (which serve as IDs) are issued by the individual states, not the federal government, and relatively few Americans ever get a passport. So, the closest things to a "master list" of people in the US that the government has are things like IRS and Social Security records - but those have flaws, too - for example, they don't count legal visitors.

I do not know what China et al do to complete their censuses.