How to begin cover letter if you don't know ANYONE

I am trying to write a cover letter for consulting positions but given my non traditional background (in biology/pre-health studies) , no known alumni, or direct connections, how should I even begin my cover letter? (After the first sentence which basically conveys who you are and what you are applying for). The standard following sentence appears to be something like.. "After meeting with Mr.Consultant at the Career Fair last week, I was particularly intrigued by your company's blah blah and I would like to join..." What can I write in lieu of that/name-dropping without sounding lame? Can I say that I read about the company's role in healthcare (as an example, based on my background) even though the position is for a general consultant role? Any ideas?? Thanks!