Prove value through your actions and then become a broken record.
1. Understand all the problems.
Most often, the role of a manager is to look at people problems not the technical ones as the people problems are typically the core issue behind a lot of technical blockages. The goal, then, is for the manager is build an accurate mental representation of the people involved, the organization, the way teams are structured, how each team works, and what the technical problems are. This can be done in a number of ways depending on your information gathering style (systematic or organic) but should be inclusive of all types of problems, not just the technical ones. This helps inform your next step.
2. Socialize yourself and provide value.
Often people expect that you are 'given' influence and that's the only time in which you have any, but this is simply not true. You can provide advice on how people can solve all types of problems in your organic conversations or your information-gathering meetings that will help build trust in who you are. This makes you a valuable member of the team and your discipline becomes a modifier as opposed to who you are.
3. Offer insight on how design could help them.
In your conversations with your team members about how certain design methodologies can help them with their problem. Note that I didn't say "try to solve their problem." For example, if the person you're speaking to is describing an issue with a roadmap, you can say, "Google runs these things called Design Sprints and it's helpful to find alignment amongst stakeholders, etc. etc. Do you think it would help you think through your problem if I facilitated this for you?"
4. Socialize design and make it available to the company.
Aside from your organic conversations, you can write value-prop documents that describe how design can help their projects and provide business case studies for when certain methods have been successful before. Ensure that your entire design team is trained on these methods and ask that they become champions for the methodologies as well doing Step #3 alongside you as they participate in the company's conversations.
5. Beat the drum, often and very loudly.
Talk. Talk. Talk. Talk about what you're doing, what you want to do, how Design is helping other industries and teams, and what value Design can provide to a business. You must appeal to the bottom line or you're going to have a very hard time selling that Design is important.
Whenever Design in the company has been used, successfully or not, talk people through the case study. Talk to them about why it worked, identify what didn't work, and provide feedback on what the team (collectively, not the Designers) can do better next time. Design is a viewpoint, not a deliverable, and your job is to teach this to your company.