You need to apply for a citizenship certificate first.
If you apply in Canada, you would need to wait until you get a letter of acknowledgement which can take a couple of months. Without this acknowledgement, Islamabad will not know that you have applied. If you apply for the citizenship certificate through Islamabad, they will know that you applied because you applied through them and they could then start processing your facilitation visa or temporary passport right away.
Right after you apply for the citizenship certificate and can prove to Islamabad embassy that you have, either because you applied in Canada and waited a couple of months to get the acknowledgement or because you applied in Islamabad, you can apply for a temporary passport or facilitation visa.
You can apply for a temporary passport without the citizenship certificate but you must have applied for the citizenship certificate already. See, you must apply, you do not need to wait until you have it. First apply for citizenship certificate, then apply for temporary passport. Getting the citizenship certificate can take several months but that is irrelevant because your temporary passport/ facilitation visa does not have to wait until you get it, you just have to have applied for it.
Therefore, I would advise that you apply for the citizenship certificate as soon as you can after your child is born and apply for it in Islamabad and apply for a temporary passport or facilitation visa at the same time. I suppose a facilitation visa would be faster but in order to get that, you would have to have another country passport for your child already.