1st day coverage depends on where they are moving from. If the person for example had landed and settled in Ontario and then decided to move to Alberta, they would not get first day coverage but would have a 2-3 month waiting period as they are moving from another province.
If they never settled in another province but come directly to Alberta from overseas, they would get 1st day coverage.
I see on another thread that you are asking about renting an apartment in Edmonton for 3 months. If your plan is only to stay in Alberta for 3 months, you are not eligible for health care. Registering for health care and saying you are planning to reside in that province when you are not, is considered to be health care fraud. If they catch you, you will be required to reimburse AB health what they covered for you which can be a lot more expensive than paying yourself up front as the hospital may bill healthcare more or differently than they bill a private person. For example, a woman in BC was asked to reimburse MSP $43,000 for a normal delivery. Her mistake was that although she did the waiting period in order to get MSP coverage, she did not stay 6/12 months in the province but left the province after 5+ months.
In addition, if they are certain that you purposely lied about planning to live in the province when you didn't, for example seen by if your landlord can verify that you asked for only a 3 month lease, you could be on the hook for fraud too and that is a criminal act.