Yes you can, however, you must have a valid job offer from a US employer and meet specific qualifications.

Yes, you can apply for a green card while on an H-1B visa through employer sponsorship or other eligible categories.

You can pursue a green card on H-1B visa through PERM labor certification or EB-1/EB-2 categories, but requires employer sponsorship or meeting specific criteria.

Your employer typically needs to obtain a labor certification from the Department of Labor, however it is very possible to apply for a green card while on a H-1B visa