How to land pre-MBA summer internship for eventual HF role?

Hi. I was recently admitted to MBA programs at NYU and Cornell. My desired career plan is CPA -> MBA -> IB Associate -> Analyst at Fundamental HF. I understand that last jump is very difficult, so I want to get public markets work experience this summer while I have time.

I'm willing to relocate to NYC, am fine with a role on the level of a college intern, and don't expect substantial pay. I closely follow the stock market and have that accounting foundation. However, I have a lot to learn about equity research, pitching stocks, and portfolio management.

How would you all approach this?

I'm thinking: do cold outreach on LinkedIn with program alumni who work at small funds; ask for a coffee chat to learn about their work; and, if they have any use for another warm body, offer to help in some fashion. (I'm not sure yet which tasks I could take on that would add any value; open to ideas here.)