Child MN1 earliest possible after my ILR (PEO)?

[t1s2010]

I have let my infant child T1-dependent expire and didn't renew as I am due for ILR.

I am going for same-day PEO service for my straight forward ILR (fingers crossed). I want to apply for my child MN1 section 1(3) via NCS at earliest possible after ILR.
We have plan to travel few months down the line once child has british passport.

Experts, can you please advice what is 'earliest' in my situation?

I guess 'if' my ILR is successful, PEO will provide me some sort of later saying 'You have ILR and you will get your BRP etc in x working days'. Can I use this letter at NCS say very next day?

Any past experience or expert view will be really helpful for MN1 for me please.

[CR001]

You will get a letter saying your BRP will arrive in x days, but the letter does not state ILR has been approved or granted. You could apply for MN1 with the letter, but the BRP would be better. All assuming the child is UK born of course.

This assumes you get ILR as a Tier 1 Gen migrant with all taxes paid and no issues in income declared to HO and HMRC etc.

[UKBALoveStory]

...You could apply for MN1 with the letter...

I did the same about a year ago and got my kids registration approved.

[t1s2010]

Awesome. Thanks @UKBALoveStory. Your personal experience makes me fully assured.

@CR001, yes UK born.
Hope so for taxes as full-time all years. All taxes paid. Only small thing (non-issue) is - I was on deputation from MNC when I came to UK; anyone on deputation needs to file SA but KPMG missed it.
HMRC never noticed. I noticed in Feb, called HMRC and they said - they never asked for SA.
Got it covered by KPMG 2011 letter saying they will handle my tax filing. Employment History matches P60 and got P11D for all years so hoping to be simple (but one never knows).

[UKBALoveStory]

Good luck