How do I write "why this firm" in a cover letter when I have no consulting contacts?

You're actually going about it wrong!

A cover letter is much more why should you want me than why I like you guys. Think about it, are they interested in hearing about how great they are, or how great you are?

Make sure your cover letter focuses on you....and you can premise it as "I value how your company is x. I am also x. Here is why"

Here are some general tips:

Step 1 - Figure out the topics for your key paragraphs. These need to be based on what consulting companies are looking for. I recommend any of the following

• Quantitative + qualitative analytical skills

• Communication (written + verbal)

• Client managment skills/experience

• Leadership

• Teamwork

• Diversity (can be working with diverse clients, teams, etc.)

• Curiosity / passion for learning

Step 2 - Once you've picked 3-5 of these, write your paragraphs

• Make them succinct (3-5 sentences)

• Make sure they lead with e.g. "x company values y, and I do too"

• Make sure they focus on your achievements. You have to sell yourself here

Step 3 - For any given company cover letter, find out what the company cares most about. Then slot in 3 of the paragraphs that fit best (again, ideally you have 5 to choose from)

Step 4 - Tweak the language of each paragraph to fit the company's website, application posting, etc. I.e. Curiosity might become passion for learning.

Then, of course, you need an intro paragraph summarizing your interest + reasons why as well as a closing paragraph doing the same with new language.