I think the most anonymous way is solo-mining. As to exchanges - there are those which don't require KYC. So if you have the skills to remain anonymous while being online your bought bitcoin will be exactly the same. p2p is arguable for me as one can get bitcoin with "dirty" history.
Solo-mining will give fresh and untraceable coins, I'm with you about this as the most anonymous way, but if the coins are old with a big history you can always use a mixer service to put them on an untraceable wallet.
If OP uses Monero and a exchange, the coins still traceable because the exchange register the operation even if the Monero Blockchain hides all the information, the exchange will have a user, mail, and IP for that transaction, so, that way isn't anonymous at all.