Many large companies will let you take an unpaid leave of absence for a few weeks or months without negatively impacting your career. I also work at a FAANG and have seen colleagues take a months-long leave for personal reasons, then come back and get promoted within a year. I've also seen people go on leave and then decide at the end of their leave to either join another team at the company or just quit and not return.

It can't hurt to ask, and going on leave rather than quitting would mitigate risks #1 & #2.