What should be the ideal strong profile contain for getting to MBB.

Typical summer placement MBB shortlist in a Top tier MBA college requires :

• Academic profile : 9/9/9 : Above 90% in 10th / 12th / UG (slightly flexible, one 8 also works) And
• UG from a top tier college - Old IITs / SRCC / NSIT
• Previous workex in a top tier company or MBB as an analyst

And/or

• National level achievements in a sport such as cricket/basketball etc etc.

Basically, have to be in the top of your field if you are targeting MBB in summer placements.

But,
In case of finals placement, you can get the short list if you are in Top 15-20 people of your batch during the course of MBA (CGPA wise) + part of a club / committee with good alumni in MBB (these vary from college to college but if you target the placement committee / consulting committee, it will be a safe bet).

Hope that helped.

Sorry, but very unlikely unless you do something extraordinary to get into a Tier 1 MBA and have an excellent spike like a national level winner of something, or sport achievement or a Limca/ Guiness world record - you get the drift.
Having been there, not sure if it's worth that effort. I had a 9/9/9, a Tier 1 Indian UG degree and a big tech job, cracked an M7 MBA and had offers from all 3 firms that you mention. I hated the mostly pointless work, poor work culture and constant bootlicking, and left. The 'prestige' that is so often glorified will require to give up on a lot that you might otherwise value. Don't make XYZ professions or companies your 'dream', more often than not, they're not worth it.