To add to this, you don't even need to know what the antibody looks like, or even if it exists. Very simplified example: It's possible to grow a dish of cancer cells (because they divide quickly and are immortal, e.g HeLa cells), "purify" away everything that isn't protein (cell lysis), then run the proteins through a gel that separates them by size (Western blot). Comparing these to a control will show you which proteins enabled survival, which gives you your candidates for sequencing and further tests.

However, right now we have humans synthesizing large amounts of antibodies that are proven to work (because the humans creating them survived and cleared the virus). It may ultimately be faster to isolate antibodies from the serum and engineer cell cultures (through adding DNA to them, "recombinant DNA") to create more of those antibodies, resulting in much stronger synthesis of a single antibody (so-called "monoclonal antibody drugs").

It's nearly certain that both of these are happening many times over around the world right now. All of the science here was already in lab use the first time I worked in a bio lab in 2003, and nowadays we have methods that didn't exist then (such as CRISPR for DNA manipulation and fast sequencing of both nucleic acids and proteins).