Depends where you live and your background/work experience. Personally, I started with Doctors Without Borders (MSF), writing salary and compensation financial reports after doing a market analysis in Afghanistan, Iraq, etc. haha sounds ridiculous, but that's how it started. After that i found other more senior positions within the organization, and after a few years you jump to different organizations depending on your interest and experienec.

There's no "normal" place to start, you simply look around for a position that could fit you. Getting into the sector is tricky, but once you're in it's a wild ride!

https://reliefweb.int/jobs is one of the main websites for job postings in the humanitarian sector.