In addition to all of the management, communication, and team building strategies mentioned here, I've got a shameless plug for a product I've been building with a fully remote team of ~30 people over the past four years: https://katmaitech.com/
In person collaboration is best, but for a fully remote company and geographically distributed team I think we've built the next best thing.
Many of us are on camera all day, others pop on just for scheduled meetings. But with the mix of working styles we've managed to maintain a pretty healthy culture, where we can have some of the spontaneous interactions that are so important.