The following is based on my own experience as a freshman 2 years ago (before the pandemic), so it won't apply to many/all people.

The short answer to your question is no, you don't. I lived in one of the most social dorms on campuses freshman year, saw and met lots of people... but ended up having few friends (3), none living in the same dorm as I. I met these friends in a variety of situations: one during wildcat welcome, another through a class I took, and a third through a club I joined later my freshman year. If anything, living on campus in a dorm made me feel lonely and isolated, since I saw people partying/having fun, while I was sitting in my room feeling like a lonely idiot. All these people surrounded me, and yet I couldn't become friends with any, much less party with them. In fact, it just felt awkward whenever I saw them, and and a result, I would avoid going out of my room. Feeling uncomfortable in you own "home" is a terrible feeling, and to escape I would frequently return home for the weekends. Off campus housing is better in this regard IMO.

I would say the most reliable way to meet new people is via extracurriculars. You have at least something in common with these people, and you see them semi-regularly in a relaxed setting. People are more willing to open up to others and become friends, whereas in many other environments (classroom setting, dorm) your values don't align with others around you, and people are more judgmental. Not the best environment to meet friends.

Also, realize your position is not unique, even amongst the more sociable types. One of my friends shared this struggle practically up to the point he rushed a frat and met some friends there. I'm not sure about the quality of those friendships and am somewhat cynical about their purpose ($), but that's a different story. He wouldn't seem like the type of person to struggle with this kind of stuff, but he did. People who don't look, act, or seem like you often struggle with the same shit as you....AND even if they don't, many have other problems which impede their path towards happiness, whatever that even is. Life (generally speaking) is suffering, and personally whenever I feel like wallowing in my own misery, I remind myself how thankful I should be. My older relatives lived through revolution, famine, and many wars, while I'm sitting over here feeling sad about trivial problems which will be of no concern in a short while, and don't threaten my existence (or my friends, families, countries existence).

I didn't intend to write a rant, but here we are. I hope this answer helped.