Thanks for reaching out.
First and foremost, I would advise you to tailor your cover letter. You can do it by talking to 2 to 3 people that work at your target firms and ask them specific questions (what makes this firm special? What differenciates it from other consulting firms (developing perople, international exposure, leveraging the intellectual capital, deep expertise in selected sectors...)
Second, you should build a story around what brought you to apply to consulting firms after x studies, y internships and z non-professional activities.
Last, do not hesitate to reach out to the platform coaches and your fellow colleagues/schoolmates in order to get feedback.
Best of luck in your application, and do not hesitate to reach out to me if you have any questions,