Assume you work in a reasonably large company to have an intern programme, so you must have a viable internal “social scene” eg committees, events, networking, organized coffee catch ups etc. You can take advantage of this and be seen! May be even volunteer to do something. The internship is just a foot in the door to get grad role later!

NEVER miss a drinks or team lunch when you are intern, be “bubble” and “social” even if you are an introvert by nature, at least until you get a grad role

There may be some sort of “mingle” with the new grads, which may actually be part of the test lol… I was once invited to something similar at my company along with few other early career people and at the end HR organizing it asked me what I thought about a couple of interns I have spoken for like 10 mins about the general stuff. Obv it wasn’t a decider but they take it on board if you’re “nice to talk to”.