My best advice would be to start small, with a single “customer” that you can work together with to build value. Depending on your org, they may well also be the people with budget to make it happen. Talk lots about your progress and shout about the wins.
In my role, I get to work with a broad range of organisations and all too often, an infra engineering team decides to build an IDP without involving any development teams in the design, build or long term roadmap. They then act surprised when devs aren’t interested.
The key metrics that you can show have been mentioned already. I favour simplicity:
time taken for a new employee to submit their first PR, time taken for an experienced employee to make a trivial change in production, and Net Promotor Score. Developer velocity is great, but a healthy respect between Dev and Ops is the ultimate goal for me.