The initial cover up didn't help either. Once they instated the lockdown, they could test the backlog of people. That took quitea while. But now the spread has pretty much stopped, while everywhere else on this planet it increases day by day.
After the initial cover-up got public, the West couldn't get enough of reporting about it, and how this is the reason it could spread so fast, how irresponsible it was, and how it's typical for evil China. Now we have that virus here, plus two month of knowledge about it, and we're still mostly being reactive instead of proactive. In China's defense, when they tried to cover it up, much less was known about the disease, like it's asymptomatic spread. Now the cards are on the table and we're being ignorant, as if ignoring a problem makes it go away. But hey, when things are getting really really ugly for us, we can still go back to blaming China for their initial cover-up.
Watch Italy closely the next days, and compare it to China when they were at a similar stage. It will tell you what's to come in your country too. Another thing that's suspicious about Italy is the high CFR of around 6%. It most likely means they're not doing enough testing, only the severe cases, so the rest wanders around the country happily spreading it further.