Unless you have U.S. citizen relatives, the path to the U.S. usually requires sponsorship by a U.S. company. The good news is that many with PhDs qualify for the O-1 visa, which avoids the whole H-1B lottery mess. You also could do a post-doc in the U.S. (typically on a J-1 visa) and then convert this to a longer term work visa or even green card.