The centralized exchanges which allow trading without KYC verification (such as Binance) only allow trading between bitcoin and altcoins - they don't allow you to purchase bitcoin with fiat without KYC. And again, any centralized exchange which offers non-KYC accounts (again, such as Binance), can and frequently does lock those accounts and demand KYC anyway.
The centralised exchange allowed trading without KYC, but I am not sure how is technically possible to buy BTC using any of Fiat payments method. it is obligatory to use a bank account for the money transfer, no matter is it directly to CEX or DEX exchange. His bank and government will know for these transactions.
I am not sure is this possible except the direct person to person trade.