How do you "prove" industry interest in an interview?

why do you want to go into finance? The best way to prove to others is to prove it to yourself and then be able to talk about it.

I would think the hardest part is landing the interview since your don't have a traditional business major background, but I'm guessing from your title you already got through the first hurdle and have landed an interview (congrats). Having a non-traditional background can help you stand out as long as you have a compelling story and can clearly explain what makes you a better candidate than someone with previous AM experience. I would also suggest doing some major prep beforehand to get a grasp of basic finance terminology and know what technicals might be asked. Staying on top of the market trends and being able to articulate where you think the market is headed and why is also a good way to prove your interest.

Ultimately no one else can tell you why you want to work in finance, but make your story genuine. You can't really pull the "I've always been interested in finance" because you clearly haven't, but interviewers can smell BS cookie cutter responses from a mile away anyways. Think of one pivotal moment when you realized humanities was not your calling and how you can still use your previous internship experience and apply it to finance.

Weave in into your story. I started premed so landing my first internship meant I had to prove interest. I explained what I didnt like and how and why I became interested in finance. As long as its genuine I think you're good.