Switching from Investment Banking to Consulting

Hi everyone, I am currently working as an IB analyst (front end) in a boutique shop. Our core focus is equity and debt funding in the startup space (seed to series b usually). Its been an year since I have joined and I am looking to switch. Joining a mid market or a bigger boutique shop makes more sense by the book and I have some connections for the same but I have been really interested in management consultancy and want to give it a shot before MBA. The thing is, I graduated from a tier 2 private college and most of the consultancy firms I know of give a huge importance to pedigree and prefer hiring from tier-1 institutes. Does it make sense for me to try getting in through referrals or is it smarter to aim for this post MBA. And to begin with, do I even stand a chance to get into some good consultancy firm?