actually we know how to produce it without involving living organism
https://en.wikipedia.org/wiki/Dimethyl_sulfide#Industrial_pr...
https://en.wikipedia.org/wiki/Dimethyl_sulfide#Industrial_pr...
Which part requires a living organism?
For a non-life explanation, you're really looking for something that could plausibly happen in (abiotic) nature, not an industrial process.
Which part requires a living organism?
haha. Do you really need a hint?