Thanks to @pebb1ee @NiJOS7@appleblossom @DDON for the discussion on the job market.
I have tried to apply in my field(research in public health). However, it seems that at present, I am a visa requiring candidate(as I just got my i140 approved for EB1a), and the process is more limited (plus any visa sponsorship fees would probably come from their grant money, which they don't want). I do have a verbal offer(via WhatsApp, he just mentioned, "Come work for me," to which I replied, "Unfortunately, I am still waiting for my green card to be processed"). Does that even count when asked during the consular processing? The PI of that team is not willing to put the offer on paper(I understand that).