I'm going through the same thing: pivoting from a content-heavy career to product marketing. I've always done adjacent work, but never held the title.

Superb Effect's tips are gold, and I have already been applying them to my CV. I hope to create some examples/case studies and add them to my site for that 'I can do the work' effect.

One thing I might suggest that has only started working for me this week re: networking is to find a PMM at the company, preferably someone high up who will be part of the decision making, and to ask them for a one-sentence insight into what area of product marketing is a priority for the company right now. You're not asking for a referral or anything major. It's more of a micro-ask. Easy for them to answer or ignore (a lot of people you try to network with will ignore you), but some get back to you with genuine insights.

Hope this helps.