Find a way to listen to what's happening around you without being overly distracting. Bias towards current projects. Here's a couple things I've done in the past:
- Sit on customer calls
- Read whatever approximates the "done recently" engineering tasks: git commits, Jira, sprint boards, whatever.
- Show up to meetings you weren't invited to.
- Take 6 different people out for coffee and ask them all the same 6 questions. Whatever you want to know.
- Sit on customer calls
- Set up the product and try to do something with it.
- Better yet, set up the product and try to do a thing a customer is trying to do.
- Did I mention sit on customer calls?
Once you know what people are working on today, it's easier to pick up and help them. Then you can start in on your own initiatives with credibility and support from the people you've helped.