How can I gain influence with Product, especialy around input into their roadmap, when they're used to operating without a Product Marketing Manager?

Other than the things already mentioned throughout my answers (relationship building, offering to facilitate planning sessions, etc.), I would also try to show them your own marketing calendar/roadmap. 

Share what you think your goals will be and ask to compare it to the rough product roadmap. Start by asking questions and sparking discussion. As you gain rapport and trust with your product teammates, they'll be more likely to bring you in at early stages, knowing that you are there to be a partner rather than an antagonist.

First off, don’t expect it to happen quickly or by brute force. Gaining influence requires trust which can only be built over time. Start with a few small wins to establish credibility. For example, market or customer insights presented at the right time in the product development cycle can be hugely influential. Showing the value of PMM is far more powerful than telling product why they should partner with PMM.

Also important is how you partner with product. Leading with curiosity will build empathy with your product team and will allow you to better position your input for them to receive. I usually start by asking a lot of questions to get a clear understanding of the product perspective. Why have they made the decision to include XYZ in their roadmap? What alternatives were considered? How much customer input was leveraged? How do they currently perceive product marketing’s value? How have they worked (if at all) with product marketing in the past? Their answers to these questions will give product marketing a sense of how and where to get started.

See my answer to a similar question on this page. You'll need to build trust and rapport with them and you do this by knowing your stuff, bringing unique insights, and having a well thought out perspective on key industry challenges. You keep overdelivering until your PM counterparts understand the value you bring to the table. If after a long period of serious investment on your part they still don't see the light, crumple your self-doubt into a tiny ball, toss it away, and find a new employer that values your PMM skills ;-)

Product is comprised of people. And so it should be clear upfront that you need to start with a foundation of trust with the people in product. Take them out to coffee. Ask about what motivates them personally. What do they want to accomplish? Who do they read/follow for inspiration and growth?

OK, let's assume you've built trust by listening. Now make yourself helpful to them as a conduit to information and outside sources that help inform them. Frame your job in terms of informing product about what's going on outside the company and in sales/marketing. Note that this is informing, not influencing at this point. 

Here are a few practical tactics you can use to provide access to useful info:

• interview customers about why they purchased and then share the notes/recording
• create a win/loss analysis report and share high-level metrics about what features are coming up in sales conversations (good and bad)
• read analysts reports in your market and provide a cliff-notes summary
• monitor competitors and send any relevant feature announcements
• record sales calls (or install sales call coaching software) so you can share specific calls 

Beware of interjecting your own opinions because if people sense you are trying to influence them then it can trigger a defense mechanism. You'll be far more effective if you can get the insights from customers, prospects, and market to shape the thinking in product. 

Remember that product is getting hit from all sides with requests and has to make tough tradeoff calls on where to spend precious time and resources. Don't become another voice in their ear asking them to listen to you. Become helpful and they'll naturally ask for more from you.

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.