After morphology, there is physiology. What media does it like, what metabolites does it produce? What temperatures does it like? Going deeper, there is the antigen signature. Use of labeled antibodies that latch onto a known antigen target can confirm a serotype.
The level of examination required for this corona virus requires breaking up the encapsulation and getting to the RNA inside. You have to amplify the tiny amount present with a polymerase chain reaction to make a huge number of identical copies. At that point you have the means to start sequencing the RNA an comparing the sequences to databases of known viruses or organisms. All of that finery was invented well after I graduated from UCSD in 1976. We did sequencing the hard way. Machines do that today.
It's not a simple process. Perhaps that's why CDC has ONE bench available and takes 6 hours to complete one test.
Ah ok. Beyond me. Electron microscope, I’ve heard of. So how are all these other countries testing while we can’t?