In general there are three options available through EB1 and EB2. In the EB1 category, significant number of postdocs apply through “extraordinary ability”, EB1A. This category does not require employer sponsorship, meaning that USCIS does not verify that you have a permanent job offer in hand. The other category which is generally of interest to postdocs, because this also does not require employer sponsorship, is called EB2-NIW, national interest wavier category.
The third category which postdocs with permanet job offers can take advantage of EB1-OR, that is EB1 outstanding researcher. The problem is most postdoc jobs are not permanent and universities or companies who hire postdocs are not willing to sponsor the green cards. However, there are exceptions when the institution calls the title as “Research scientist” and treats them as permanent employees.