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
Great tip thank you. I have never really thought about going to an BTC atm before, I will use one soon now.