You are a intern, they are full-timers / You are much younger than they are.
I'll have a look from the other side of the lense as, for years, I've been on the other side: much older than the team (at the workplace) or the student (in my own company). It might be useful to understand how it works from another point of view...
What did I expect? As a newcomer, to become part of their group, or, in case I already was in the place, that they feel welcome and become part of my group.
What were the expectations?
- feeling good together whenever possible.
- do a great job as a team.
- teach or learn new things (yes! elders and full-timers can learn from younger and kind of inexperienced folks / newcomers!).
Wait! But that's just what you want to achieve too! :)
How did I manage that? Just trying to be as nice as possible...
But it takes time. You can't break through right away. You first need to know the other one(s). Do they talk a lot or not? What are they interested in? Do they like to talk or just keep silent?
As for you, I could meet my colleagues for 2 / 3 minutes each hour, at the coffe machine, or at lunch time. Anytime I had a chance, I would just ask something nice: how is it going? Need anything? Where can I find this? and so on... My best advice is: don't start with something personal, keep it professional, but nice, in a way that, either you offer help, or ask for help.
This is the first (and major) step: if they see you as a nice and helpful guy, they/you just opened the door. From there, you'll have opportunities, they will come to you much more easily. And they/you can start the small talks.
I did that when working with up to 38 different nationalities mixed together (European / North American / Central and South American / Asian). And the age range was 20 -> 50. We pretty quickly found the ones that would gather together, and small groups were born...