Thank you for your insight! I have had several short internships with non-profits in the field of public health. And it does seem like that contacts and unpaid internships is the way to break into the field. As far as the UN is concerned, I am (unfortunately in this case) from the country with the largest population in the world.
However, I want to clarify something you mentioned which is NGO don't compete for H1B quotas. I believe they do, unless it is a not-for-profit organization affiliated with a university, or a primarily research-focused NPO where the foreigner's job title is "researcher". I believe that those are the only two categories where NPO would be H1B cap exempt, which does not mean that they will be waived from the H1B application fees, either.
Just out of curiosity: is it typical for the NGO that you are working in, or any other NGOs that you know of, to hire foreigners for their US office if they were exceptional?
Thanks!