How to network in your late 20's?

I am currently working in the family office space. I've been here for almost 3 years and have done well, but I've lost my interest and motivation to pursue this career any further and would like to move into a role more involved in the capital markets. I have reached out to a friend of mine who is a director at a MM bank. They passed my resume along to a member of his team, who is responsible for hiring. It's a waiting game now, but want to get more irons in the fire. He mentioned targetting roles where I could get some transaction experience which has led me to look into the Big4 (deals, corp fin, transaction services). I don't have any connections at these firms but was wondering what is the best approach to reaching out to people at the Big4 in these divisions? What job title should I be targetting? Given I am 27 most people are probably around the same age or younger than me.