No - in fact from the start I would not allow him to gamble or try to gamble, so that kind of case will not happen. I don't want to be another person who allows their underage children to gamble instead of preventing it. Underage gambling is prohibited and should not be done under any circumstances - but perhaps some parents might consent to KYC documents if there's a large win waiting to be withdrawn.
What you are saying is that in a situation where you are aware, you can stop the child from gambling, and it will not get to that point again where there will be a need for you to offer your details for KYC verification, but now that you are only finding out when the child has already gotten a winning, it's left for you to either offer to pass KYC and get the winning out, or you abandon it because of your principle.
Supporting underage gambling is when am aware that the kid is gambler and I didn't stop him or her. In this situation, I was not aware that the kid was secretly gambling, therefore if they had a massive win, instead of letting the money to waste, I will offer to let them use my details to pass the KYC but after withdrawing the money, I will keep it in a savings account for the kid until he or she comes of age and I will also make it a duty to stop the kid from every gambling activities since am now fully aware of their gambling activity. I will make sure to deprive the kid from gambling until he or she is 18+. Another method I could use to handle such a situation is to deprive the kid from gambling and let the KYC hanging like that until they get to 18+ when they can have their IDs and pass the KYC.
Your last idea is not favorable if you ask me, because you can't predict what will happen to the casino from now till when the child will reach the age of majority before using his documents to pass the verification, and even if that happens, it's very likely that the casino will also detect that during the time that the money was won, the child was an illegal gambler, and they can deny the child the withdrawal since it's against policy for an underage child to gamble.
There is difference between supporting something and event that has already happen. If it's by law, the money belongs to the child and since the parent is responsible for everything the child does, then parent has a very valid reason to stand for any responsibility that comes after and as for the KYC, there is nothing wrong but for gambling, the parents has the right to take any action against their child, it's left for the parent to correct their child for the wrong doings.
I get your point; if it's by law, the money belongs to the child, but if we also follow the same gambling law properly, the child has violated the casino policy, and it is found the money will no longer belong to the child, which is what also makes the issue a bit more complicated, since it's an event that has already happened. Offering the help, which is something almost all parents will do, is a must, but that's also somehow robbing the casino.