How to win staff+ level ICs to support my promotion case

Hey 👋

I am an L5 engineer working at a fast-growing company with ~1.4k engineers. I focused a lot on growth towards staff engineer responsibilities (using Taro a lot!) and now my manager would like to put forward an L6 promotion case and he supports me fully in this. Not sure how this works at other companies, but we'll need to ask feedback from at least L6 ICs in the org and also find champions for my promotion case.

I heard that it is particularly important to find champions that are well-respected by senior management because these promotions are ultimately decided higher-up.

I was recommended a few L6 & L7 ICs by my manager who are strong veterans in the org and my manager mentioned that it would support my case greatly if I could have their support. The problem is that we are working on quite different domains and rarely had the chance to collaborate in our day-to-day work so far.

How would you build trust and gain the respect of these individuals in this case to ultimately have their support for a promotion case?

It also feels a little weird to come up with some artificial way to collaborate just to ask for their support for a promotion, as our day-to-day work rarely intersects.