Earlier there were some exchanges in which trading or withdrawal could be done before doing KYC but now the exchanges have become a little stricter so now KYC must be required for trading or deposit withdrawal. If you talk about good quality exchanges, then the first name that will come is Binance and KuCoin, you can easily create an account in these two exchanges, but if you want to deposit, withdraw or trade, you need to do verification. Even so, verification is not a very difficult task, if you submit your information correctly, your account will be verified within two to five minutes. As it is about money, I think it would be a good decision to submit KYC and then trade or deposit.
KYC is an important factor in cryptocurrency transactions. Still some exchange sites don't make KYC mandatory but I think every platform should do it. In the case of cryptocurrency transactions, we use a common platform, if there is ever a mistake in storing some of the secret keys of that platform, then if KYC is done, there is definitely a security guarantee. KYC is mandatory in top level exchanges. There, KYC matters are followed thoroughly, though it needs few moments to complete KYC. On the other hand some platforms don't want KYC but I think they will definitely want KYC today or tomorrow. Recently MEXC platform does not require KYC and it is still recognized as a good exchange site.