"Start to develop a vaccine" can be a rather hazy claim in the age of mRNA vaccines (even though these are still largely experimental.) Simply downloading the RNA code of the virus (posted by the Chinese) can possibly count as "started to develop [mRNA] vaccine".
It would be interesting to know the more detailed timeline of the development of (first) US mRNA vaccine for Covid-19, but alas I could not find details on its very early stages of development, to say exactly how much work on it was already being done on Jan 11.
Briefly mentioned in a Turkish source (but probably correct):
Moderna drug company based in Boston, U.S. on Jan. 13 announced it developed a potential vaccine called "mRNA-1273", two days after China announced the genetic sequence of COVID-19.
According to Moderna's own timeline:
On January 11, 2020, the Chinese authorities shared the genetic sequence of the novel coronavirus.
On January 13, 2020, the U.S. National Institutes of Health (NIH) and Moderna’s infectious disease research team finalized the sequence for mRNA-1273, the Company’s vaccine against the novel coronavirus. At that time, the National Institute of Allergy and Infectious Diseases (NIAID), part of NIH, disclosed their intent to run a Phase 1 study using the mRNA-1273 vaccine in response to the coronavirus threat and Moderna mobilized toward clinical manufacture. Manufacture of this batch was funded by the Coalition for Epidemic Preparedness Innovations (CEPI).
I could not find where (and to whom) NIH disclosed that (intention to run Phase I trials) on Jan 13. (There are not NIH press releases between Jan 10 [something on alcohol] and Jan 15 [something on health disparities]. The next NIH press release that mentioned coronavirus was on Jan 23, and this seems mainly intended to highlight the JAMA paper by Fauci et al. In fact, I think this was the first official NIH press release that mentioned the novel coronoavirus.) That JAMA paper published on the same day, (Jan 23, but surely written before that day) mentioned that:
Vaccines, which have adapted approaches used for SARS-CoV or MERS-CoV, are also being pursued. For example, scientists at the National Institute of Allergy and Infectious Diseases Vaccine Research Center have used nucleic acid vaccine platform approaches.
During SARS, researchers moved from obtaining the genomic sequence of SARS-CoV to a phase 1 clinical trial of a DNA vaccine in 20 months and have since compressed that timeline to 3.25 months for other viral diseases. For 2019-nCoV, they hope to move even faster, using messenger RNA (mRNA) vaccine technology. Other researchers are similarly poised to construct viral vectors and subunit vaccines.
Furthermore, by mid-March 2020 such (mRNA) vaccine for Covid-19 had started Phase I clinical trials in the US:
A Phase 1 clinical trial evaluating an investigational vaccine designed to protect against coronavirus disease 2019 (COVID-19) has begun at Kaiser Permanente Washington Health Research Institute (KPWHRI) in Seattle. The National Institute of Allergy and Infectious Diseases (NIAID), part of the National Institutes of Health, is funding the trial. KPWHRI is part of NIAID’s Infectious Diseases Clinical Research Consortium. The open-label trial will enroll 45 healthy adult volunteers ages 18 to 55 years over approximately 6 weeks. The first participant received the investigational vaccine today [March 16]. [...]
The vaccine is called mRNA-1273 and was developed by NIAID scientists and their collaborators at the biotechnology company Moderna, Inc., based in Cambridge, Massachusetts. The Coalition for Epidemic Preparedness Innovations (CEPI) supported the manufacturing of the vaccine candidate for the Phase 1 clinical trial.
The announcement for that (Phase I) trial had been posted to ClinicalTrials.gov on February 25.
(Also of some relevance here, in mid-April BARDA announced it was financing (to the tune of $483 million) the Phase II and III trials for this particular mRNA vaccine. BARDA is part of the HHS, but not part of NIH though. Almost certainly coincidental, but BARDA's director was fired the next day after that announcement.)