Somewhere in my thirties....I finally made MYSELF break the introvert mold. I'm so sad I didn't do it in my 20s when I was always sitting off in dark corners of parties with a very few close friends MORTIFIED to go meet people. Finally I realized, I LIKE people. I like knowing people. I'm nice. Many other people are nice. I simply MADE myself become outgoing, or at least approach and smile and talk to people. Now it's more natural after years of just doing it. In my 40's I can be that confident person who just goes up to people and meets them and walks away with a new acquaintance or friend if we hit it off. I still naturally prefer intimate small gatherings, but I have a LOT of friends and acquaintances.
The key is to ASK OTHER people about themselves. Stay engaged, show interest, check in, make invites, accept invites, be nice....you know the drill. But you're right, it doesn't happen on it's own, and sometimes I feel like I'm the ONLY ONE making an effort. But it does work. It's never as natural as for some (my good friend knows EVERYONE and can talk to ANYONE-I'll never be her).
When you see that new person and cringe (I know the feeling:) Just breath deep, change your stance, and approach. Good for you for noticing this! You can do it!