IIM Ahmedabad or any other IIM does not consider the type of college the candidate belonged to as eligibility criteria. So rest your worries and apply for MBA in your dream college even if your undergrad BBA college was a less reputed one. Regarding your undergraduate college, the only criteria are the minimum marks for appearing for the CAT exam i.e. 50%. All you need to do is get an excellent CAT score.
To get admission to any IIM, you need to focus on things like CAT score, 10th, 12th, Bachelor grade. The school and colleges from where you acquired your education do not matter at all. What matters is that your academic profile should reflect your excellent scores and involvement in extracurricular activities
So, appear for CAT, aim a 98.5+ percentile, and get admission to IIM Ahmedabad. What’s stopping you?
Firstly IIM Indore does not offer BBA but BA in Foundations of Management. And yes, you can leave IIM Indore after Bachelors. You can then attempt the CAT and apply for top IIMs. In Fact it is a good decision.
I can also provide you with an example. Last year in CAT 2020 an IPM student from IIM INDORE scored 100%ile and then moved to another top IIM. This might motivate you to finalise your decision.