Your understanding of timeline is based on what we know today.
China only know about unknown pneumonia cases in the last 2 weeks of December and by 31 December they discovered that its a new virus and shared to WHO which means to the world.
The first 2 weeks of Jan 2020, there were a lot of unknowns. There were more cases coming in but they were not sure how it was being transmitted yet. That was why WHO sent out the controversial tweet on 14 Jan about no evidence of human to human transmission yet but now everyone accusing WHO of lying for China. The fact is it was only 2 weeks since the discovery of the new virus and nobody know for sure how it is spreading yet.
By the 3rd week of Jan 2020, China got evidence that it is spread from human to human via airborne. That is why WHO informed the world but nobody take it seriously except a few countries that suffered SARS before such as HK and Taiwan. By the 3rd week of Jan 2020, China already lockdown Wuhan and later the whole province and the country. However, it was too late as Jan is near to CNY and most people in mainland has already balik kampung or go on vacation. A lot of foreigners who work or has biz in China also will go back to their home country during this period due to the long CNY holidays.
As for the earliest confirmed records of patient in China, nobody know for sure as nobody know about Covid before end of Dec 2020. However, using methods from conservation science, analysis suggests that Covid probably arose between early October and mid-November, 2019 in Europe and China. How did this conclusion comes about?
The WHO team assessed medical records from more than 230 clinics across Hubei, the province where Wuhan is located to look for clues. More than 90 patients in the province were hospitalized with pneumonia or coronavirus-like symptoms in October and November 2019. China own investigation confirmed that the first case in China is probably on 17 November 2019 but you must remember that they only discover this through back testing as the disease was unknown at that time.
A study from Milan's National Cancer Institute also found that four of Italy's coronavirus cases dated back to October 2019. Italy recorded its first official coronavirus case in Lombardy on February 21, 2020. Yet a recent study found coronavirus antibodies in blood samples collected from 23 Italians in September 2019 and 27 in October 2019. Italian researchers also found the coronavirus' genetic material in sewage samples from Milan and Turin dating back to December 18, 2019. In May 2020, doctors at a Paris hospital discovered that patients they'd treated for pneumonia on December 27, 2019, had been sick with COVID-19. however, France didn't record its first official case until January 24.
Research in the US, too, offers evidence that the virus had gone global before humanity even knew it existed. The US recorded its first coronavirus case on January 20, 2020. But according to one study, the virus had reached the Pacific Northwest at least a month earlier. Blood samples collected by the American Red Cross in nine states, including California, Oregon, and Washington, showed that some Americans had coronavirus antibodies as early as December 13, 2019.
So where did you get the info that China still haven’t provide the medical records of the patients affected during Oct 2019 hence already lost the chance?
