It's easy building relationships within your own team but how do you build relationships across other teams whom you do not work with on a daily basis?
Good question! My main advice is to make sure that you get the maximum value from each of the few interactions you do have with them. Have inviting body language, communicate in a friendly way, offer to help, think about their incentives, do all the necessary things to earn trust. I recommend these to help with that:
Aside from that, provide tactical support where you can. Review their code and answer their questions, especially when they touch your team's codebase. Become the go-to person they go to whenever they need to interact with your team and anything it owns: Developing that identity as an incredibly ambassador is a big part of going from senior -> staff.
If there's an office you have to show up to, honestly just eat lunch or dinner with people. Even if you eat with the same people, people will naturally change teams so that'll spread out the teams you talk to. The people I normally eat lunch with went from 2 unique orgs to 4 unique orgs within less than a year.