as mentioned by Vlad it is unusual to join consulting doing an MBA straight after undergrad; normally you can join MBB either after undergrad or grad school. You could also work for some years, ideally for second tier consulting companies, strategy roles or in banking, do an MBA and join MBB for a post MBA role.
In terms of the elements to consider in your CV, for undergrad the elements used for screening for consulting interviews are normally the following (in order of priority):
- University reputation
- Academic performance
- Work experience
- Extracurricular activities
- Experience abroad
The probability to be invited for interviews will depend by the previous elements and by the presence of referrals. You can find some more information on that below:
After the invitation, you will be evaluated on your fit and case performance, your chances to land an offer will depend on that. If you join after undergrad (or grad school in some countries, pre MBA) you will join at entry level position (Business Analyst at McKinsey, Associate at BCG, Associate Consultant at Bain).
Hope this helps,