Ok, I am having a hard time following your timeline. You have been working as a caregiver in Israel for the last 5 years, before that you studied to be an elementary school teacher but didn't do that because you got a job as a cashier for 4 years? And after working as a cashier, you went to Israel to work as a caregiver?
When did you plan to work as a food counter attendant in AB?
If you did get a job and a work permit as a food counter attendant in AB, you could be sponsored under semi-skilled PNP but that is the only way to get PR with that occupation. It is also dependent on the employer meeting certain requirements, wanting to sponsor you and that they are not sponsoring too many other people at the same time. If you get sponsored by such an employer, you must stay with the employer until you get your PR.
Another way to get your PR, since you already have more than 1 year of caregiver experience, you could get a job under the live-in caregiver program. After 2 years of doing that, you could apply for your open work permit and PR. The processing time keeps getting longer but you would have to continue to work as a live in caregiver until you get your open work permit. After that you can do what you want.
You can not apply under CEC with a low or semi skilled job. You can not apply under FSW if you have no skilled work experience. You would not get enough points, besides, you'd need a skilled job offer.