I would strongly recommend to always start with your strongest argument, i.e., what YOU bring to the table. Your motivation is rounding off your storyline.
So here is a structure that tends to work very well:
0. Subject line which clearly indicates the purpose of the letter (i.e, application) and the position
1a. Short first paragraph* outlining ~3 central requirements that you believe are needed to excel at the job you apply for (--> ask yourself "what makes an excellent consultant?" --> https://www.preplounge.com/en/consulting-forum/what-makes-a-good-management-consultant-1710)
1b. Second paragraph where you give evidence how your skills, experience, and track record lead to a strong match with exactly these previously outlined requirements
2a. Third paragraph outlining your motivation to work in consulting
2b. Fourth paragraph outliningyour motivation to work at the specific firm
* If you use a referral, you can start the cover letter with a short sentence where you mention the corresponding person within the firm.