J-1 visa holders subject to the two-year residency requirement need a J-1 home country physical presence waiver before applying for a marriage-based green card. The J-1 visa waiver removes the two-year home residency requirement.
You may qualify for a waiver if you can demonstrate:
Exceptional hardship to a spouse or child who is a U.S. citizen or lawful permanent resident if you had to leave the U.S. You’ll need to provide evidence that your absence would cause extreme hardship.
No objection from your home country’s embassy. The embassy must state that they have no objection to you remaining in the U.S.
You would face persecution in your home country due to race, religion, or political opinions. Note: this is different from an asylum claim.
A U.S. government agency requests an extension of your stay for purposes specifically related to your field, such as completing your education or continuing work on an important project.