There are a number of KYC-Free P2P trading platforms in the following list:

Person-to-Person bitcoin Trading Platforms https://cointastical.github.io/P2P-Trading-Exchanges

But that doesn't mean this is anonymous. If you buy when paying with Interac, for example, your counterparty (the seller) will know some of your info as the sender. Depending on the platform, the platform itself might see the payment details you were provided in the chat.

In-person, cash trading can be the method which preserves your financial privacy the best, but there may not be sellers in your area. Cash by mail may work.

If you don't see an offer, and are not needing to trading right away, you as buyer can place a BUY offer and possibly a counterparty (a person wanting to sell) will take you up on your offer. Offer to pay an amount above spot if you want to persuade a seller to emerge.