The Newbie's Dilemma in City Hall

I recently moved to a new city and started working as an intern at the local government office. Everything seemed great until I realized my coworkers were all long-time friends who had formed cliques years ago, way before I showed up. They have their own inside jokes and casual conversations that exclude me constantly. It's not outright rude or mean, just that they don't seem to make an effort to include me. On the first day of my internship, there was a coffee break where everyone got together for some light conversation. I tried to join in but ended up feeling like an outsider. They talked about their weekends and shared stories from past office events, all things I couldn't relate to since I just arrived here last week. It made me feel so out of place that I ended up sitting alone on the stairs outside, looking at my phone instead. I've tried a few times since then to break into conversations or make small talk, but it's clear they prefer hanging out in their little groups rather than interacting with someone new like myself. This morning was particularly tough when one of the senior employees left a note asking us all to contribute cookies for an upcoming team lunch next week, everyone signed up except me since I wasn't invited to participate initially. I've been here less than two weeks, and already I feel so alienated from this place where I'm supposed to spend my days learning. It's hard not knowing if it's because of something I did or how I present myself that they don't include me in their activities, which is really the only way for us interns to get to know each other beyond our work assignments. I suppose I could try harder, but after so many failed attempts, I just feel like a burden. Maybe moving here was a mistake and I should have stayed at my previous city where everyone knew me better.