That sounds familiar.
Four years ago DD was upset that the rest of her first year flat went looking without her, and was not reassured when I suggested that plenty of rooms would come up between then and the summer.
She played University sport so mentioned it them, and a couple of others said the same had happened to them, so they decided to look together, and picked up a flat just before Christmas when many bothers had gone home.
It worked well. They had not known each other well but had interests in common and a similar lifestyle. (Freezing pitches rather than warm clubs!) One is still a close friend.
DD agreed I was right about rooms coming up. There was a lot of fallings out through the year , and indeed her first year flat mates apparently had massive ructions in the middle of their second year. Others will drop out or fail their first year exams, with one good room coming up in the summer because someone had to take a year out for medical reasons.
It is worth focussing on lifestyle. Problems seemed to occur when some in a group settled down in their second year and cut back on the parties, whilst others continued.
There are alternatives if nothing works. Though something will. DD, who is a medic so around for longer, took last year out to study for an intercalation degree. Because of Covid, no one was moving and with finals coming up, she did not want to share with strangers whilst most of the non medics had left the City. There were quite a lot of private halls options aimed, I assume at international and Masters students. (We bit the bullet and she is renting on her own. Oddly student accommodation where she is, is more expensive that non student accommodation which normally comes up a month before vacancy. )