Honest question - if you worked at Facebook or google as a SWE, do you need referrals to other companies? Isn’t it pretty easy to get a call back from other companies without one?
Referrals can also help tip the scale if they are on the fence about you, depending on the company and the quality of the referral
It only tip the scale if the referer actually know you and have worked with you.
Just reach out to recruiter on LinkedIn or apply in careers section. Considering you have FB on your resume you should hear back!
Why leaving FB ?