H1-B visa transfer during 60 day grace period after job termination

[sameer.gupta.phx]

I was on h1-b visa with company A and it terminated my job last week. As per my understanding I have 60 days to find another job as per recent 60 day grace period rule. However as USCIS is currently not doing premium processing, will I be able to join new company based on H1 filing receipt it self ? Also what documents I may need to submit to prove my termination ?