We already know where did this pandemic originate from: China. But do we already know who was the first person infected and when did this person contact the virus? Were scientists able to determine this?
According to an article from livescience.com which can be read here, doctors and scientists managed to trace back the origin of the virus to a 55 year old person, who contacted the virus on Nov. 17, 2019. Even though this Nov. 17 case was identified, doctors can't be sure that this individual is the so called "patient zero," or the very first human to have been infected with SARS-CoV-2, and there's a chance even earlier cases will be found.
In another article on cbsnews.com (article here), it is mentioned that tracking down COVID-19's patient zero and how that person first contracted the coronavirus may take years, especially as U.S.-China relations tumble to a new low.
In conclusion, the short answer to the question is: no, unfortunately we don't know who is the patient zero of this pandemic.