The real first question you should be asking yourself is how can you empathize with product. Just as with your role and other PMM roles, Product Managers and members of the product team are swamped with suggestions, demands, and interjections regarding how they should go about improving their processes. This can be draining and frustrating.
Once you are able to level with your PM and their team, this is your foot in the door to communicating ideas more effectively. You should also note that when you are influencing a person, manipulation won't work - rather you will have to communicate in a way that makes sense to everyone.
The best way to do this is providing hard data, numbers, and outcomes that will highlight your input. If you are trying to make your ideas come to life simply because you feel it is the right thing to do, you are far less likely to have your voice heard.
So remember, first you have to be human, and then you have to be a human who has numbers supporting them. Once you have that down, you should be able to at least have a productive conversation.