Actually reading the contemporary NBC News https://www.nbcnews.com/politics/politics-news/tom-bossert-t... and Washington Post https://www.washingtonpost.com/news/to-your-health/wp/2018/0... articles the Snopes piece cites in the body, they seem to have been a handful of people in one team in the National Security Council hierarchy, that the new National Security Advisor reassigned to related agencies, as part of a desire to have his own hierarchical structure. Ziemer resigned because he wanted to keep his team the way it was.
COVID19 was not a surprise; that is, it was known to exist in China some time before the first cases appeared in the US. It is not unreasonable for a government to assemble a team to respond to something like a pandemic as needed, as opposed to having people dedicated solely to the purpose and nothing else. And that's exactly what the US did, implementing the ban on non-American travelers who'd been to China in late January, among other things.
You may or may not agree with this. But please don't claim that this is somehow prima facie proof of the Trump administration's malfeasance/evilness.
PS - No, Trump did not "cut the CDC budget" either. https://apnews.com/d36d6c4de29f4d04beda3db00cb46104