Each virus has identifiable traits that make them different from others. When you have people with new symptoms and contagion methods, you know you're dealing with something new, so grab the blood of many people with similar symptoms, you put their blood under a microscope and you can see what they have in common when compared to healthy blood. You also compare it to other viruses.
https://www.sciencealert.com/this-is-what-the-covid-19-virus-looks-like-under-electron-microscopes
https://www.flickr.com/photos/niaid/albums/72157712914621487/with/49531042877/
You don't have to look at it directly, though. When you're dealing with new symptoms, new forms of transmission, etc., you know you're dealing with something new. When a virus infects a person, it also affects the surroundings. You can look at the antibodies, for example, and by examining them, you can notice whether a person has been infected with COVID-19 in the past, even if they are already "cured".
https://www.cdc.gov/coronavirus/2019-ncov/testing/serology-overview.html
There are petabytes of reference information against which these samples can be compared. Everything from chemicals, antibodies, previous vaccines and drugs... you can apply many tests and arrive to conclusions about the nature of a disease (viral, bacterial, etc.), the origin, etc.
The testing procedures they use are not designed to identify a virus.
What do you think about that?