@OrangeBunny provided some comments. Those are definitely things you can/should do. But I think it's unclear whether you can count upon this working.
What you would really want is some
legal decision or document declaring the father the sole guardian - or equivalent wherever you are. This will depend on the locality and possibility of actually getting this concluded; in many jurisdictions this would mean attempting to contact the spouse, public notices, etc. (Obviously if the father does not currently reside with the child, that may make things more different).
You might also wish to apply for TRV for the child. If she gets approved (chances may actually be quite low), at least she would be with the family while this plays out.
But: you do not say the exact age. As soon as she turns 18, IRCC will no longer require this permission. It may be a bit chancey to apply before she turns 18 but given processing times, it may be a moot point by the time she actually gets considered for exact eligibility and final approval.
Personally if no legal docs are feasiblle, I would proceed as suggested above - explain that the mother is not around, all of the other points; possibly petition/start the process to at least attempt to get sole legal guardianship (although I know nothing of the process in India);
and refer explicitly to age of the child and that you anticipate she will be a legal adult by the time the application is approved.
Note: this is not a guarantee it won't be rejected. But an IRCC officer may decide it's not worth rejecting on that basis since it will be a non-issue in a short period of time.
