I got an entry-level job at age 52. I began learning to code, rather casually, at age 47, and began coding daily at age 50.
Yes, it's harder for people in this age group than for the young, but I am evidence that it's possible and would say persistence was the most important factor in my case.
I had a pretty big portfolio of projects by the time I got hired, but I don't think it played any role in getting me a job. However, building that portfolio certainly enabled me to improve my skills, and it was a tangible expression of my level. Confidence in my level is part of what got me hired.
Taking part in an open source project was often recommended to me. I joined one late in the job-hunting process, actually just before getting hired; it played no role in my getting work, though.
It's also important for the candidate to make use of the skills from their prior experience. Your friend's degree in Mathematics means that data science and numeric programming are much stronger possibilities than others.
And of course networking widely increases one's chances very starkly. I don't think going to Meetups and conferences was very helpful to me. Two batches at the Recurse Center established a phenomenal personal network for me, and that network gave me a lot of support and got me a few interviews, but not a job. What worked for me was to contact people I already knew (mostly in fields other than programming) and ask whether their companies have programming positions or whether they were close to any engineers whose companies had programming positions. In the end that was what worked for me — the husband of someone I hired long ago is an engineer and recommended me internally. But relying on one's network is slow; it worked for me because I was able to persist long enough.
People in this age group are part of the neglected long tail of the job market, and I take seriously my responsibilities toward other people in the group. So I'd be happy to speak to your friend, if that would be useful. I can be reached at the email address your friend will find at the bottom of this link.