Do what you can at any point. Do what you can, and don't beat yourself up.
Thinking about speaking or not speaking to people is over-thinking, in my opinion. It is enough to say "hi" to someone in passing or sitting next to you, or the person giving you your coffee. That's what taking the initiative in life actually looks like. "Hi". Maybe later it looks like, "Hi. How are you?"
We talk about and read in the therapy that we should act, take the initiative, and do first. This works against the anxiety. It's when we don't do that we help build up the anxiety again.
Getting to know people - this may be more involved. But also, getting to know people starts with a "hi". Nothing more than that. Making friends is a series of hellos and small talk. Don't build it up.
If saying "hi" to people is where you are at, that is good. That is where you are at. Do that. Don't worry about a club or hobby. Take all the small steps you can, though.