How can I get more involved with people at work? I wouldn't want to come off as desperate of course and I am not. However, I feel it is important to do it here especially since I anyway know very few people outside of work.
Depending on how large your organization is! If it is a larger one, chances are that there is something organized (at least in germany this is true) like doing sports together. If so I'd say this would be the best place to engage in, because this would give you the opportunity to spend time away from work the work context with your people. If the organization is quite small this might not be possible. But on the other side in smaller organizations it should be more easy to get in contact by inviting to drinks afterwork or make appointments for lunchtime.