Internships are about learning, so you need to convince your administrator that you will get a valuable learning experience. "Learning by doing" is a cliche that probably won't be enough for your administrator. Universities have a mindset that connects learning directly with teaching (not doing). They aren't completely wrong on this, in that good learning comes from doing things properly and teachers can often define "properly" for you.

My recommendation would be to join an accelerators or incubator program. That gives you the mentors/teachers necessary to satisfy the "learning" requirements of the university. Alternatively, try to find experienced partners for your stand-alone venture (sort of arranging your own private accelerator program).

As a last resort, maybe you can get a traditonal internship in an established start-up that relates to your space. You could then pitch your project within that start-up. Who knows, they might pick up on it.