Not used one myself but if you want to be completely anonymous you could use a Bitcoin ATM, I believe you just need a wallet address. You can find a list here -
https://coinatmradar.com/, other option is to buy them locally and in person from someone. Personally I've used Bittylicious which has worked well, you do need to verify your identify though
I do agree with this since when you use bitcoin atm there are no registrations needed and you only need a bitcoin wallet to receive bitcoin. But there is nothing wrong with submitting a compliance on KYC and AML if you are not doing something wrong. But to the author if you have a good reason as why you need to be unknown then use a bitcoin atm.
You have someplace for your bitcoin to actually go to once you have a wallet. To connect your credit or debit card to your wallet is a convenient way to get it done quickly. But its defend on what bank and card you use to determine when its done.