I think they had a good grasp on the problem, but the problem to them was (as it always is for China’s leadership) firstly about maintaining control, and at best secondarily about dealing with Covid.
People have been saying, for years, that the ‘wet markets’ of exotic animals are breeding grounds for inter-species diseases. The Chinese government did not listen to these complaints for many reasons, including the fact that ‘medicinal remedies’ made from exotic animals are a status symbol for upper-class Chinese.
Moreover, the only reason why China's covid19 outbreak threatened the Chinese regime's control over the population is because the Chinese regime failed to address the problem in a timely manner after intentionally turning a blind eye to the problem, and afterwards attacking it as a political threat instead of a public health crisis.
Between covering up the fact that their death rate was a few orders of magnitude higher and deciding to intentionally leaving out infected but asymptomatic cases from their infection statistics while boasting that new cases occurred due to infected foreigners entering the country , it's patently obvious that the Chinese regime does not and never had a good grasp on the problem.
And if that does not convince you, let's not forget that the Chinese regime's talking heads tried to pin the blame of their outbreak on Italy.