Most of the ones I know have been hired by Google, straight out of a program called Google Summer of Code (GSoC) which prepares students for this and they instantly get referrals if they complete their project.
Now if I were starting out right now I would look at tackling the first contribution issues in smaller projects, then work your way up to the larger projects. I’d say contribute to a project that you even use yourself, improve it and branch out from there to fix issues in its dependencies / libraries.
Also the GSoC website has lots of participating organisations [0] to contribute to.
My personal favourite orgs are
LLVM, Linux Foundation, Xi Editor, Haiku and Blender.