The facts, and their timeline, make the answer to this obvious. Yes, he did, and to a much greater degree than the Democrat party, which was focused on trying to find impropriety in a diplomatic phone call at the time. But you can't tell that for the simple reason that the press is indeed, sadly, largely fake news. They consistently lie (See: What More Proof Could You Want?) and don't care that it's easily disproven, because they know most people won't bother to do the research to realize they're being lied to. A lie that is spread far and wide for 24 hours, is disproven and then quietly dropped from the news cycle, is an extremely effective and efficient form of slander, as well as their stock in trade. 

 Here is a timeline of events, taken from both the Congressional Record and press reports, covering the period from Jan 6th through March 16th. This is the period sometimes misrepresented as Trump's "lost months" in the coronavirus battle. (My primary source is this Deroy Murdock piece.)

 
  Trump Administration Actions Democrat Party & Congressional Actions
Jan. 6 CDC issues Wuhan, China travel notice, before the first US case. Democrat House is out of session
Jan. 16   Trump impeachment trial begins
Jan. 17 CDC begins Covid screening at 3 major airports (JFK, LAX, SFO). US Cases still zero. Impeachment trial continues
Jan. 20 CDC opens an Emergency Operations Center for Covid response after the first US case is reported. Senate & House out of session
Jan. 21 CDC expands Covid screening to 2 additional airports (ATL, ORD).

House meets for 2 minutes (to fulfill legal requirement to do so?)

Senate rejects Schumer's ammendments to impeachment

Jan. 29 President Trump convenes & announces the Coronavirus Task Force  Impeachment trial continues
Jan. 31

The day after WHO declared Covid a "Public Health Emergency of International Concern", President Trump severely restricts travel from China.

CDC begins mandatory quarantines.

HHS declares "a public health emergency in the United States".

 Biden calls travel restriction, "hysterical xenophobia".

Senate declines to call witnesses in impeachment trial.

House is out of session.

Feb. 2 CDC adds Covid screenings at HNL, SEA and IAD airports. Senate & House out of session
Feb. 4

FDA removes beaurocratic obstacles, allowing use of CDC's Covid test in non-CDC facilities.

President Trump delivers State of the  Union, saying "My administration will take all necessary steps to safeguard our citizens from this [Coronavirus] threat."

No votes taken in Senate or House.
Feb. 5 White House Chief of Staff briefs Congress on Covid-19.

Senate acquits President Trump of impeachment charges, primarily along party lines.

House Foreign Affairs Committee holds Covid hearing.

Feb. 9 Coronavirus Task Force briefs National Governor's Association  House & Senate out of session. 
Feb. 11 HHS coordinates with Johnson & Johnson to develop a Covid vaccine. 

 Senate confirms a judge to federal bench.

House passes "Smithsonian Women’s History Museum Act".

Feb. 18 HHS offers funding & expertise to "Sanofi Pasteur" (world's largest dedicated vaccine development company) to develop Covid vaccine & treatments.

 Senate out of session.

House convenes for 1 minute.

Feb. 19 Trump assigns VIce President to lead US Coronavirus response. 

Senate out of session.

House passes 2 pieces of (unrelated) legislation and orders study of Chief Standing Bear Trail.

Feb. 29

FDA removes beaurocratic hurdles, allowing ~2,000 labs to begin development of Covid tests.

Covid related travel warnings issued for South Korea and Italy, restricts arrivals from Iran.

 House & Senate out of session
Mar. 3 Trump makes morale appearance at NIH's Vaccine Research center 

Senate health committe holds hearing on "How the US is reponding to Covid-19". 

House passes (unrelated) act and resolution.

Mar. 6  Trump signs $8.3B Covid response bill passed by House & Senate over previous 2 days. House & Senate out of session 
Mar. 11 Trump restricts European arrivals  
Mar. 13

Trump:
... declares National Emergency
... deregulates telemedicine to facilitate ongoing health care during epidemic
... deregulates interstate medical practice & physician hiring at hospitals
... gets Walmart, Costco, other major retailers to commit to drive-thru testing stations

FDA permits development of Covid test kits by Roche, Fischer companies

Senate out of session.

House passes $192B Families First coronavirus relief package. 

In other words, the Trump Administration was acting early & often, sometimes behind the scenes, before the press and Democrats ("but I repeat myself") show any particular interest in Covid, about 2 months later.

Mr. Murdock concludes his article with these observations:

Could Trump have done more, sooner? Yes. By definition, every evening that he did not moonlight at the Vaccine Research Center, unpack test tubes and rinse Pyrex flasks was an evening he could have done more.

But while Trump did plenty to fight this plague early, Democrats largely toyed with impeachment and then dozed off once their magic wand failed to make him disappear.

They now should stop whining, concede their own comparative sloth and recognize that President Trump has led the federal government and inspired the private sector to battle a health care challenge unlike anything America has confronted since 1918’s Spanish Flu pandemic.