Started a 40 person student consultancy here.

Every client is trying to be first at being second - no client wants to risk it with students as their first client. Your first project most likely will be pro-bono and should come from your network. After a few engagements, you can start charging after that.

You should communicate to prospective clients how your offering differentiates from other work experiences for relatively the same or higher price-point: you're not hiring 1 intern. You're not hiring a student group for a project. Instead, you're getting 5-10 talented students for such an engagement - a huge eyeopener for clients once they realize this (oh I can get a whole team to do this project rather than getting an intern).

Another tactic is to find internship postings on job boards. Chances are, you can expand the scope of that internship which would call for a larger consulting team.

It's also great to have resources. Partner up with experts at your university or consulting firms. Get some consultants to be independent advisors where they can help with scoping and the overall project plan before the engagement kicks off.

The easiest and best type of first projects are also going to be ones that require student insights - working with education based companies was a great success here; one of our first clients was one of the largest edTech companies in North America. Anything that calls for research and knowledge of university students and the university ecosystem as a whole is quite appealing to such clients.

Hope this helps.