There is a ton of great content on Taro already about this already, but it's a great topic and would love to bring it up again for discussion.
The #1 best thing I did was organize game nights and movie nights, and participate in rock climbing and happy hours when the company was in person 4.5 years ago and I was a new engineer. I did this just because I wanted to have fun and get to know people. Pretty soon I realized it made it way less awkward to ask for help as a new engineer to someone I went rock climbing with last night and was ordering Thai food with later today for movie night. Not only that, but these events included sales, marketing, design, product, ops folks, and company leaders from time to time - so I learned how the business worked and built relationships that made me feel at ease when I needed to collaborate with anyone.
Recently in a 250 person remote situation I've filed my calendar with checkins ranging from 2 weeks to 16 weeks that are just "coffee chats" (I think I got this from Alex!). With fellow engineers, recent joiners and long time coworkers, we sometimes pair program a bit, or talk about the product, or just talk about life! What's been awesome then is some people that I do coffee chats with have ended up directly working on the same thing as me later and then we can really hit the ground running. But even if not, it's great to have someone to talk about work challenges with both directions.
So basically my advice here has nothing to do with the technical part or even any tactics related to communication. Rather just this: care and show up for people.
I did a lot of random things at Pinterest which helped me build deeper relationships with coworkers (almost none of these are related to software engineering):