Look, the issue of how you support the child financially is one thing - a separate matter.
I'm surprised at this outrage - even if you were to 'fix' this right now, it likely wouldn't make a bit of difference.
Now note, this is all basically my informed speculation:
Let's consider you reporting it yourself to IRCC, with whatever docs you can provide and an apology that you didn't understand because you weren't on the birth certificate or whatever. First, this is nothing new to IRCC, they don't have much info, whether they take your apology at face value, there's not much they're going to do save decide whether further action is required. No, they're not going to expel a PR (with family, if that was even possible); they're going to make a note to file that you didn't report child X and that child can't be sponsored by you in future. That's it. That's all the 'further action' that would result at present.
End result is no different than not reporting, because if you apply in future whether the child is disclosed now or not, they'll see you didn't disclose the child before when you should have.
Someone else reports it? Sure, there's an allegation. Perhaps some evidence. But there's no application to sponsor, nothing they can do about it, so they're going to ... possibly make a note to file that you didn't declare a child on your app (name, whatever info they have) and ... that's it. They can't even likely prove it because not on birth certificate. Even if they conceivably could, they are NOT going to investigate some hypothetical situation - no resources to pursue futile dead ends.
No different result. In all cases, IRCC is not going to do anything until they have a reason to, which basically boils down to some attempt to sponsor the child - which is not remotely possible in current circumstances (custody).
If that changes in future - well, look into it then.