See my answers on gaining buy-in from resistant functions and 30/60/90 day priorities. The most important thing to do, especially in an environment with a less experienced management team, is to educate everyone internally about what product marketing is, what your impact will look like, and how it should be measured. In less structured environments, it can be helpful to manage through metrics. That is, pick a differentiated metric that is not necessarily owned by another function as market penetration within a particular customer persona/segment, transaction density by geography, etc, and report regularly on that. This lends more weight to the processes and strategies you want to put in place.
Additionally, I would establish cross-functional meeting cadences dedicated to demonstrating your processes to the rest of the org. They can quarterly competitive intelligence shareouts or monthly GTM roadmap reviews or both.