IIM Indore - Indian Institute of Management

No, BBA being a Bachelor's degree can be pursued only after class 12th. If you want to start with management at an early stage after your class 10th. You can go for Diploma in Business Administration. It will be of 3 years. And after Diploma in Business Administration you can go for BBA lateral Entry which is of 2 years rather than normal BBA which is of 3 years. It will be advisable if you do your degree from a well-known university and that provides prime placement opportunity, outstanding industrial exposure and professional enhancement training. I am enlisting some of the top colleges for your help such as:
Lovely Professional University, Sri Ram College of Commerce (SRCC), Delhi Lady Shri ram College for Women (LSR) Delhi, Hansraj College Delhi, and Loyola College Chennai etc.

Because I am an IIMian with commerce background.
You have to clear cat cut off, perform well in interview.
If your CAT score is same is that of an engineer guy (I am not saying science, because there are a few people who are from science background other than engineers) your probability of getting into IIM is high. All IIMs give weightage for academic diversity and in a few IIMs like Trichy, there are different weightage for each background and commerce background has highest weightage.
The next big category after engineering background is from commerce background. (Percentage of engineers in IIMs start from 76%, then 10% is more than enough for second place and most of IIMs engineers accounts for more than 76%).
Participate in competitions, Do well in cat, prepare well for PI - revise all things you studied in B.Com, remember your graduation scores matters a lot.