The decoding is done by "whole genome shotgun sequencing" -- e.g. breaking up all the proteins in a slurry to smaller pieces, detecting each piece and analyzing it, and reassembling the pieces in a computer. So you can take something that includes the virus and produce genomes, but doesn't require isolation. I don't think this "isolation" argument is critical to understand whats going on.

Also, SARS-CoV-2 is a positive-sense single-stranded RNA virus, which means it has very high mutation rates, and infections are always swarms of related-but-not-identical genomes. So isolating a "single genome" is difficult, not that meaningful. See https://harvard2thebighouse.substack.com/p/a-grin-without-a-cat