The only advice I can share is that customer insights (when shared in a clear and actionable way) are very hard to ignore. Survey users, talk to prospects, and bring customer insights to the product teams, even if they aren't solicited.
I thought I'd share a recent example from Stripe: a few months ago, one of my teammates was paired with a product group that was moving very quickly to deliver an MVP to the market. Because they were moving fast, they didn't invite marketing input. Synthesizing some of the challenges she was piecing together from members of the product group, my teammate was able to quickly survey dozens of prospective users via email and shared the results broadly. The team found it so valuable that they shifted their priorities, added features to the roadmap, and even asked to run more surveys.
It can be tough to change organizational culture, but the only way to earn a seat at the table is to have data or direct customer feedback that provide a unique perspective or that aren't otherwise available to the product group.