Realistically, you would need someone to vouch for you, and a skill set that is applicable to the lab you are joining. We have post-doctoral fellows on visas in our lab, but they're pretty extensively vetted and they all bring something productive to the table. We love to train and teach and help get FMGs to their next step, which is often residency, but we aren't running a charity. Research money is not easy to come by, and funding a fellow even at $45,000 a year costs more like $65,000 with fringe and institutional overhead, and I could fund a faculty co-investigator for 3 months of effort for that kind of money. It's a help me/help you situation. I get at least 5 form letter-style emails with attached CVs every week from people looking for positions, coming from all over the world. I delete them all, because it isn't that hard to find people that have already been evaluated by PIs I know and trust.
The trick for you will be getting your foot in the door, doing potentially unpaid work for someone until you've proven your worth, and then parlay that into a lab talk and a letter of reference with someone who has money to hire.