Uhm, censuses are described in the Bible - in fact one has a central enough role that even a committed heathen like me is aware of it -, and existed many places on a similar timeline. I have no problem believing that they were imprecise, and not widespread enough to give good global numbers, but they had certainly been invented much earlier.
There's also the Domesday Book (https://en.wikipedia.org/wiki/Domesday_Book), which wasn't an exact census but it did log 268,984 people considered to be the head of a household; based on this and all the ifs and buts around the number, they estimated the population of Wales and England in 1086 between 1.2 and 1.6 million people.
Herod's census was a tax thing too. Censuses are very expensive, and only even vaguely reliable if you threaten people with dire consequences for not taking part properly. So they don't often get done for funsies.
The Roman Empire had a motive to take a census (for things such as taxation of its subjects) and the means to enforce it over a wide area, neither of which survived its fall.
