First of all, I’m super transparent about the genesis of my idea. In my experience you’ll lose credibility quickly if you aren’t upfront about the fact that you don’t have a ton of data to support an idea you’re passionate about. Hopefully, you do have at least some good reason for your instinct. Have competitors successfully done something similar? Do you have research or user feedback that would tangentially suggest your idea will work?
Next, be precious about the problem you’re trying to solve, but not about the specific implementation you have in mind. In other words, you should aim to convince stakeholders that there is a problem worth solving, not to convince them that solving it with an email (for example) is the only possible way to do it - there’s never only one way to solve a problem.
Finally, see if there are any cheap, easy ways to test your idea. Can you get some users or customers on the phone quickly? Can you do a quick test in product or a copy change that would give you data on whether there might be demand for your idea?
On the Consumer side (where I sit) we have Brand Marketers and Product Marketers. Product Marketers need to deeply understand the value prop, positioning and user needs of the product. A big part of the PMM role is Inbound - leveraging research and insights to influence product strategy. When a PMM has Outbound work they need to do, we work very closely with our Brand counterparts to ensure our campaigns are consistent with the overall Brand message, and don’t conflict in terms of timing and channel.
I’ve been in consumer businesses during my career as a Product Marketing so I can only speak to working with Product. I’ve had a lot of great experiences with Product partners.
First and foremost, when starting a new business relationship I find ways to add value before I start offering criticism. Figure out what the team needs that you can help with and start there for at least the first few weeks.
Next, make sure you’re picking your battles, and make sure your rationale for picking your battle(s) is anchored in some kind of insight (ie. this is the most important thing to our users and the research shows we’re not meeting expectations yet).
Lastly, best practice for influencing will require you to tailor your communication to your audience - figure out how your key product stakeholders make decisions and build your case to fit their style.
Build a RAPID (or choose your decision making framework of preference). Ideally, this isn’t such a problem in your organization that you need a RAPID for everything. But don’t waste time trying to backchannel this and figure out whose opinion really matters - be transparent and ask your manager or stakeholders to partner with you in clarifying this. It is absolutely best practice at any company to be very clear about who the decision maker is (as well as the other roles in the framework) - you will be doing your company a huge service to insist on transparency in identifying these roles.
The advice above is for the actual decision making process. But I also gather input to improve my work. Find folks in the company who have successfully led cross-functional projects and see what you can learn from them - what would they do differently next time to drive alignment faster and more effectively?