Summary: "The best approach is to purchase through an acquaintance whom you have known for long and feel safe to deal with. Or buy online... to make a purchase, you need to make payment using bank transfer or e-wallet."
Is that really anonymous, then? I don't think so.
Then you mention Bitcoin ATMs, but they almost always require ID. They all have HD cameras to record your face and eyes, too. I don't think Bitcoin ATMs are private in any way. If you can find one that is, please tell me about it! I've never heard of one.
"Fill your prepaid card with cash and then use it during peer-to-peer exchanges"
What's a prepaid card? It would have been nice if you had explained what that is, or how to get them.
As far as I can tell there are NO ways to get Bitcoin privately and/or anonymously.