How likely is it someone in there 20s who barely goes outside and has no family history gets melanoma that young?

It certainly is not impossible-especially if there is unprotected sun exposure. Hopefully, the melanoma was caught early and they are getting treated. If the diagnosis is in question, a second opinion may be helpful. Best of luck to you!

Rare, but unfortunately possible, all diseases we see are the result of genetic predisposition and environmental factors, many times hard to pinpoint due to limited knowledge and individual complex variability.