The privacy of a deposit is only as good as the coin that funded it. Coin bought from an identity-checked exchange and sent straight to a market ties your name to the deposit. These routes avoid that.
In-wallet swaps
If you already hold Bitcoin, a wallet like Cake can swap it to Monero through an integrated provider. The provider sees the addresses but not your identity, and the swap breaks the direct trail from an exchange to the market.
Peer-to-peer
Peer-to-peer platforms let you buy coin from another person with a range of payment methods and a random identity rather than a verified account. Fees are modest and the privacy is far better than an exchange withdrawal.
The point
Break the link between your real identity and the deposit address. Route through a fresh wallet you control, or swap into Monero, before the coin ever reaches Awazon.