If you put no registered sim card in and if you bought the phone cash and anonymous in a regular shop, and not online, where the seller connects the imei to the buyer, you have full privacy.
To keep it, don't put personal data of whatever kind on your phone and don't put private data in whatever you do online. If you log into your bank account or search for the same things with same pattern like you used to do on non private devices, your phone loses privacy.
Things like Tor might masquerade your ip, but only technically. You never know which node you connect to etc, so Tor is more a theoretical thing than truly providing anonymity.
If you only want to hide from advertisers and trackers, you can use adblockers that run systemwide on a local vpn.
VPN in general don't give you privacy. They even minimize it, because they are always connected to a specific user, whilst no vpn on public or shared networks makes you still identifiable, but without any specific account.
In General, if you don't want to make something public, then don't make it public. Every pidgeon sending a letter is more private and anonymous than any internet device ever can be.