You do not need to know anyone in Canada in order to be considered for permanent residency (although having immediate family members in Canada can increase your chances of being eligible for consideration).
The general consensus among members of this forum is that illegal residency in and subsequent deportation from the US shouldn't* disqualify you from consideration (*although a criminal record could, so if the deportation was also accompanied by an arrest and/or conviction or something that could negatively impact your boyfriend's criminality assessment, that could be grounds for a refusal).
Note, as well, that you cannot apply for your 'boyfriend' as a member of your family, unless he meets the criteria for being considered a common-law spouse.
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If you do not think that anything in your common-law spouse's background would render him criminally inadmissible (keep in mind you'll have to provide police reports to prove this and a full background check will be conducted), then your first step is to find out if you or your spouse are eligible for consideration for Canadian permanent residency, under the Express Entry programme.
Unless you have 1-year of full-time Canadian work experience, you would most likely be trying to apply under the Federal Skilled Workers (FSW) programme.
If you are NOT eligible under any of these three programmes, you are unfortunately not eligible to apply for permanent residency through Express Entry (but there may be other ways for you to pursue permanent residency – these additional ways will not be covered here).
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If you ARE eligible under one or more of these three programmes, please note that this does NOT guarantee you will receive an Invitation to Apply (ITA) for permanent residency. Your likelihood of receiving an Invitation to Apply is dependent on your
Comprehensive Ranking System (CRS) Score.
The CRS Score is what IRCC uses to determine which candidates will get an
Invitation to Apply (ITA) for permanent residency.
The general consensus is that, at least at the time of writing this, you need a CRS score of at least 435 to have a chance at getting an ITA; but please note that this could easily change in the future.
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If you are eligible, and you have a decent CRS Score, I would recommend visiting the Canadian government's website, as well as reading through the threads on this forum (especially sticky threads) to learn more about the Express Entry programme and how to apply. People on this site are always very willing to answer any questions you might have, but there's too much information involved to rely on the members of this forum. The onus will be on you to try and learn as much as you can with the information that is available.