There's a formula I've bookmarked from someone to help you get better social capital. In order to increase your surface for social capital you need to expand your influence, therefore you need to increase your luck:
L (luck) = D (doing) x T (telling)
Basically, you need to be able to show you are able to do stuff (D) and with enough people seeing this by you sharing (T) through different channels, can open doors. I haven't been doing it as heavily but it has already given me incredible opportunities.
Best way to have social capital is an introduction into a space where money and power exist. Many spaces no matter what you do you will never be able to get in without an intro, and they have extremely few opportunities. Being college buddies with a member of an upper class is one of the only times they will ever socially mix. It is indeed like royalty in every way.
Being at Harvard gets you a lot relative to the population, being around the right clubs at Harvard gives you a lot relative to that. There is meritocracy within the range but nepotism can easily put people in the room. Work at a startup or two run by families of billionaires, and watch their career trajectory, and you will not have any doubt.