Most elite educational institutions have their own Marketing Team, which handles even their digital strategy, including promotional material and digital presence.
In fact those who have the money (MNCs and their subsidaries) hire graduates straight out of NID, IITs and IIMs to handle their marketing and growth strategy , so trust me it is not an easy environment to infiltrate.
This is where your networking and communication skills come into play.
When it comes to any niche subject like graphic design / web design / consulting of any kind it pays to be observant , even if ignorant.
Getting a sense of what is the industry standard (minimalism /contemporary / responsive/ cross-browser), how to network with design professionals BETTER (more proficient) THAN YOU, and a persistent , articulated approach to celebrating design principles on your OWN WEBSITE will be a start.
You also have to play the patient game, and have a long term approach to be a top notch Design Consultancy.
At the risk of repeating myself, NETWORKING IS KEY!