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I wonder if really Canadian company hire foreigners via LMIA. I used to work for a telecommunication company as a Technical Analyst and my hubby as Project Manager, Both of us were PR before and my son is a Canadian citizen. Due to some unforeseen reason, we went back to our home country and could not return back to full fill the number of days, hence we did not meet the RO. We did appeal and our case was dismissed.
Now I am trying my best to return back to Canada for the best interest of my child
 
I am not sure, I need to check my CRS. What is the best score for selection ?

Is there such thing as non express entry ?

Yes, there is such a thing as non express entry through the provincial programs - PNP. You would need to have a job offer in the province to generally qualify.
 
I wonder if really Canadian company hire foreigners via LMIA. I used to work for a telecommunication company as a Technical Analyst and my hubby as Project Manager, Both of us were PR before and my son is a Canadian citizen. Due to some unforeseen reason, we went back to our home country and could not return back to full fill the number of days, hence we did not meet the RO. We did appeal and our case was dismissed.
Now I am trying my best to return back to Canada for the best interest of my child

Some companies do. Many however are not willing to go through the process.
 
I think it's the age only, cos I when I purposely choose 1982, it immediately creates a reference code with the same information which I provide and select with my actual age as 1974.

In that case it sounds like you do not have enough points to meet the basic requirements.
 
I wonder if really Canadian company hire foreigners via LMIA. I used to work for a telecommunication company as a Technical Analyst and my hubby as Project Manager, Both of us were PR before and my son is a Canadian citizen. Due to some unforeseen reason, we went back to our home country and could not return back to full fill the number of days, hence we did not meet the RO. We did appeal and our case was dismissed.
Now I am trying my best to return back to Canada for the best interest of my child
So your only options is ITA through Express Entry with a score well over 500, LMIA with approved closed work permit or PNP with job offer. Honestly, your age is not in your favour and getting a LMIA is difficult even for younger people. Having a Canadian child gives you no points or ”ins” to return.