- Legally you still can break this contract, they will not sue you if you do it in a polite way
- You'll have to give back the sign on bonus if you have one
- You'll never get a job in this company again (and in any company that this company acquires)
To mitigate the consequences you should:
- Be transparent with a tech firm that you want to move to a different company
- Explain your reasoning
- Talk openly not only to HR but also to the manager of the team where you were supposed to be hired
- Be very polite
But you should think twice - do you really think MBB is a better place than a Big Tech nowadays?
If you want to work in Tech in the future - I would go there directly. If you want to be a consultant / pursue some other career - move forward with MBB. Keep in mind that consulting option will always be with you.