It's a gradual war, not an overnight battle. Gain credibility by continuing good work.
1. People first, good design second.
Initially, you're likely not going to do good design work, but that's okay. Instead, focus on bonding with the other teams and care about their problems. Winning their respect is the main objective here.
2. Develop emotional resilience and persistence.
Don't set your expectations high, or you're just going to get frustrated. Don't stress out about things out of your control, just keep calm and keep doing good work.
3. Develop good credibility.
Gaining trust and confidence of others in your team will happen over time. Once you have enough trust and credibility, you can get more resources to drive better design outcomes.
4. A list of Don'ts
Don't spam design thinking workshops. Don't try to justify the importance of good design ALL the time. Don't believe that design is the most important thing in the company. Understand where you are in the ocean of things.