So the purpose of your group is to help people to socialize? and you want to find ways to monetize that?
I'm not sure if you can monetize a Facebook group directly. Many people have a website where they post up links to it on their Facebook group page. On your website, you can put up affiliate links. Clickbank for example, have products that help people overcome shyness and anxiety, etc. You can become an affiliate for Clickbank and put affiliate links on your website. There's no guaranteed you'll make money but it doesn't hurt trying.
If you don't want to use Facebook PPC Ads, you can join related Facebook groups, and be active there and try to befriend people, then ask them politely to join your group over time. This is the long-term strategy. I would recommend using Facebook Ads for short-term build up however.