They have in fact isolated and documented the covid genome of different variants. It's the same as reading and saving the human genome, or the flu, or bacteria, or any other organism. There's multiple journal articles from multiple countries about isolating the virus and saving the genome. Then they do the same with people who are sick and compare the genomes. This is pretty basic biological science stuff.

We isolated virus from nasopharyngeal and oropharyngeal specimens, and characterized the viral sequence, replication properties, and cell culture tropism. We found that the virus replicates to high titer in Vero-CCL81 cells and Vero E6 cells in the absence of trypsin. We also deposited the virus into two virus repositories, making it broadly available to the public health and research communities.

From the US: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7239045/

From Korea: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7045880/

From Turkey: https://pubmed.ncbi.nlm.nih.gov/32936826/

From Australia: https://pubmed.ncbi.nlm.nih.gov/32237278/