You don't need to H1B to apply for green card.

You can probably go through labor certification. IDK how easy it would be go with cook/manager. You have to prove that there is no local US candidate who can do the job you are doing and you cannot use any experience that you learned on the job as a requirement.

I would check the website http://dolstats.com/ of approved labor certifications. I have seen cooks and managers as a profession that has been approved.

I work in IT and am in student status and doing my GC through I-140.

@m00se
I have been working with state government in permanent full time position for past 3.5 years and they are willing to sponsor me for a GC while I am in TPS. So, do you mean I can't use 3.5 years of experience from this state job and I have to use experience before joining this job?