You could choose another site to use seems like you are registering to a site with a KYC required to use their service there are so many other providers that you could use without having a KYC.
can you state few of those exchanges that do not require identity verification before buying crypto with fiat?
Most if not all regulated exchanges will ask you to verify your identity when you make a fiat deposit/withdraw.
Even decentralized exchanges like bisq aren't completely anonyous when it comes to fiat trades. You will have to provide some personal information such as your name and bank account.