Hey!
I think you certainly have a chance, but I think leveraging the referral is going to be your best bet. Is there any alumni of your university that you could also reach out to for help/guidance/potentially a referral? Two always better than one!
If you’re confident in your preparation and feel like you can perform well, go for the interview now. Curious as to what would be stopping you? Would you not finish university until next year? In which case unless you're interviewing for a internship position they'll suggest you apply next year anyway.
Best of luck and let me know if I can be of help!
Will