Guide to break into firms that don't actively hire intern

Hey All,
 

Eager to break into Commercial/Corporate Banking, however, in the area I live (APAC), there aren't many bulge brackets or boutiques that offer internships in this field of Banking. We do have tiny offices for a few Asian Bulge Bracket (HSBC/MUFG/ICBC), but browsing through Alumni and LinkedIn, I can see no one has actively interned at these places.
Was wondering what are the best ways (if its even possible), to reach out and see if I could temporarily join as an intern just to gain a bit of experience? Should I first try to network with some of the junior analysts, associates, MD, or reach out to their HR?

With these APAC bulge brackets, HR ultimately decides who works and doesn't work at the firm, so a bit conflicted. We had a family friend whom was an MD at a Bulge Bracket in Singapore which was keen on having me work for a short stint to get a taste of the industry, but was turned down by HR since I was a foreigner and figured I wasn't worth the hassle of getting a short visa to legally work there (even if unpaid).
Part of the reason I'm aiming for Corp/Comm Banking is because it's a lot more niche, so a lot less competitive opposed to IB, and they're on the same floor in many banks :D. Any advice would be appreciated!