I would start by saying that it is unfair to blame the President for any of these things, except of course, for his irresponsible rhetoric. However, since we know that Trump wouldn't have hesitated to politicize this pandemic and go on Fox News and completely blame Obama for it, had this outbreak occurred 5 years ago... to an extent, Trump is fair game. So, with that in mind:
What could have been done differently?
1) Epidemiologists and infectious disease experts were advocating for more Americans to self-quarantine and to cancel social events in early February. However, President Trump held steady to a dismissive tone on the coronavirus into March.
2) As other nations, such as South Korea, tracked and prevented new infections by testing tens of thousands of people, the CDC had administered fewer than 500 tests in February. Trump's claim that "anyone who wants a test gets a test" was and still is, horse manure. Dr. Anthony Fauci has called the fed's testing program 'a failing'.
3) President Trump's team ignored an alarming shortfall of basic medical supplies, such as masks, hospital beds and ventilators necessary to handle an expected surge of patients requiring hospitalization and the Trump administration fought with governors who were openly requesting the White House to release federal funds to aid in preparation efforts. Regardless of what Trump claims to have said, he was dismissive of this threat in February. He basically blamed it all on a media overreaction designed to tank the markets and damage his reelection bid. It was irresponsible and paranoid. He also accused any governors who were critical of his response (or lack thereof) of partisanship.