H1B is a nonimmigrant visa category. You can start a green card process without H1B, though based on the following employment-based preference category:
The Employment First Preference EB1 category is for “priority workers.” These include persons with “extraordinary” ability, outstanding professors and researchers, and managers or executives of multinational corporations.
The Employment Second Preference EB2 category includes persons with “exceptional” ability and professionals with an advanced educational degree or equivalent experience.
The Employment Third Preference EB3 category includes certain professionals and skilled or unskilled workers.
The Employment Fourth Preference EB4 category is for certain special immigrants. There are many subgroups within this category, covering highly specific professions and circumstances.
The Employment Fifth Preference EB5 category is for immigrant investors. To be eligible in this category, a prospective immigrant must invest, without borrowing, a very substantial amount of money in a job-creating commercial enterprise in the United States.