It is all about knowing individual engineers inside these companies. Nearly any engineer in FAANG can, with a little effort, donate their own work time to an opensource project in the form of submitting patches.
The project can help in various ways. Make sure licensing stuff is in place so that whatever IP review process the company has goes smoothly. Make sure PR's are reviewed fast. Delegate responsibility ('hi, would you like to be maintainer of this feature?'). Make sure contributions are publicly recognised (ie. Public page of maintainers/biggest contributors).
Remember that most engineers inside big companies are trying to generate good content for their performance review. "Wrote and open source some code" is usually one of the checkboxes.