Yes, the president did know how severe this was in Jan, Feb, and March and he lied to American people and did every thing in his power to downplay it, ignore it, and oppose measures to impede it. To Trump, the virus was an existential threat to his re-election so he tried to deny it and downplay it and ended up in a battle against the the US healthcare authorities.
Trump certainly knew about. His intelligence people were briefing him weakly. All reports from China and the WHO indicated a major new virus. His medical advisors were warning him and he did nothing to prepare the country.
The WHO Outbreak News published on Jan 5th contained a risk assessment.
On Jan 10, the WHO issued a warning an immediate preparations that should be taken.
China published the genetic sequence on Jan 12th.
On Jan. 14th, WHO's technical lead for the response noted in a press briefing there may have been human-to-human transmission of the coronavirus (in the 41 confirmed cases).
On Jan. 13th, 14th, and 15th, the first cases outside of China were discovered in Japan, South Korea, and China.
On Jan 20th, the first confirmed cases outside of China was confirmed
On Jan 22, the WHO issued a
statement saying that there was evidence of human-to-human transmission in Wuhan.
On Jan 30th, the WHO Emergency Committee, issued a Public Health Emergency of International Warning.
On Feb 3rd, the WHO releases the international community's
Strategic Preparedness and Response Plan to help protect states
On Feb 16th Deeply concerned both by the alarming levels of spread and severity, and by the alarming levels of inaction, WHO met with over 400 representatives around the world to discuss the seriousness of the virus
On February 28, Donald Trump announced that the virus was just the Flu and that democrat warning were just a hoax.
On February 28th the first outbreak in the US was reported.
On March 1st Donald Trump announced the virus was under control.
As of Oct, 28th there are have been over 9 million cases in the US and 235,000 deaths