There are many casino sites that offer KYC free gambling and allow you to deposit and withdraw up to certain amount without any Kyc verification. so in this case you will not have any problem even if you do KYC later. But when you go to gamble with a big amount you definitely need KYC verification. But it is better for everyone to play gambling without any kyc with a small amount on a site first and gain experience of that site. Then if any site seems good and trustworthy then complete kyc then gamble with a big amount. It can be a good strategy to research gambling sites
If an online casino needs KYC verification it's better to complete it first, The idea that you can still withdraw a certain amount without KYC is not acceptable by me, such a casino can one day say you should have known better and the fault will be on you.
If it's a No KYC casino then you are free to do anyhow with deposits, but if pass KYC is available on the casino please make sure you pass it first, OP is making some sense, some casinos can be picky on identities you provide, you can believe that your passport is the neatest and nothing can decline it, what if a casino denied it?
The first thing you will think is, it's because you have deposited some money, that they are planning to steal that money, but you have forgotten that it's their space, and you have to bide by their rules, if they say no to your passport it stays a no.
I think it's best to always pass KYC if the online casino asks for it, to avoid stories.