The Chinese might well be lying about the virus, but to see what likely happened there, we can figure out by take a look at the facts as we know in the West, which are undisputed.
1. In the U.S., while there were handful of cases, it really took off in about mid Feb. By the end of March, we are staring at tens of thousands of cases with multiple epicenters. That is with social distancing in effect around mid March and the media blasting 24/7. We see similar trajectory in Italy and other European countries. Once you got a few hundred cases, it ramps up very quickly.
2. Unrestricted travel while the virus is in the population mean it would spread to every state in the U.S., We are seeing this here. In less than two months time, we are looking at hundreds of thousands of cases in multiple epicenters.
3. The Chinese are as interconnected within China as the Americans are inside the U.S. You can take a high speed rail from one corner of the country to another.
4. The Chinese told the world about this at the end of 2019 (Dec. 29th).
5. The Chinese New Year is Jan. 25. Travel is the heaviest a week before that.
6. The Chinese locked down Wuhan on Jan. 23.
With all these facts, it is possible to see how long China (or the local government) managed to hide the true extent of the problem. We know with high certainty that travel restriction was not enacted before the lock down, or we would hear about this in social media. In a country the size of China, you simply can't enact travel restriction secretly, especially around Chinese New Year. We know that there weren't multiple epicenters in China, or the lock down would be extended to cities in other provinces. If the virus had started circulating at the beginning of Nov., with three months of unrestricted travel, you would definitely see it spread across much of the country with multiple epicenters. They could still contain it, but would have to lock down many other cities in other provinces Wuhan style. The numbers of dead in other parts of China would skyrocket. With the world looking at them intensely since the lock down, we have seen a handful of cities being locked down in the Province of Hubei but not outside it. Using a similar timeline as the epidemic happened in the West, we can deduce that single cases probably started popping up by early December and it really started with hundreds of cases by mid December. In the most egregious scenario, they withheld the information for about two weeks.