Start by lowering the immediate objective. Your first goal is not 'get a referral'; it is to have a useful conversation with someone who has enough context to eventually assess you.
Use alumni from adjacent schools, previous employers, clubs, competitions, geographic ties, or second-degree connections. The non-target consulting guide covers ways to create access when campus recruiting is limited.
When a relationship becomes strong enough, a referral may happen naturally. The strong consulting referral guide explains why credibility matters more than simply having a name in the system.
Keep messages short, specific, and easy to answer. A low response rate is normal, so consistency matters more than trying to write one perfect cold message.