You develop social capital by fostering relationships with other people. By being responsible, and having positive interactions. You'll develop that capital not just with them, but also with the people around you and them.
If you have a positive relationship with someone, and they think well of you, then their friends and family and colleagues will accept their voucher (assuming they have a positive relationship with those people).
You want to do this starting from zero? I've done it, though not with the intent of developing social capital. I was just tired of being lonely.
Seek out people to do things with. I started attending mass again. I went to Bible studies. I joined a soccer team (I sucked at soccer, still do). I went to movies and dinners with people. When they invited me to an event, I'd say yes unless I really had something else to do (could legit be cleaning the apartment, but usually meant travel or work or obligations to other people).
Be responsible, be honest. When they invite you and you say yes, you show up. Do not be a flake. You will get a reputation as a flake and your social capital will go down the drain.
As you meet more people, foster deeper friendships and connections with those who it makes sense to. Do not force it. Several people I met this way had very similar technical interests to me, we developed a stronger connection over that and I got a new job. Others have similar academic or travel or other interests, and we connected over that. Others, we just have mutual respect for each other and cared about the other's wellbeing.
Take charge. Initiate and plan events. Doesn't have to be all of them, but some of them. Don't drop a hint, "Wouldn't it be fun to go to the beer festival this weekend?". Send out the invitation, do the planning. Set the times. People show or the don't. Start doing this, they'll start showing. And when they don't, let it flow over you. Don't take it as a personal rejection (even if you may not it to be that). Enjoy the day, and meet people at the event.
Over time this becomes more natural if it feels weird at the start. And don't think about it from a social capital perspective. Just focus on the doing things with other people, especially things you enjoy, aspect.
And once you have the initial circle, especially if you take ownership of it by leading the call to gather and do things together, it'll expand. People will bring in people from their other social circles. Some will stick around, some won't. Merge your various circles. I have colleagues and friends, I invite both to movies and things. This moves people from the "associate" or "acquaintance" categories to the "friend" category when we hit it off. Sometimes they bring people and those are the ones I connect with.