Make privacy a USP
All products need a reason to succeed, beyond basic brand loyalty. Also known as a "unique selling point" to marketers.
So do what Google won't do: make privacy a big deal.
Make your default to block/separate tracking cookies, avoid browser fingerprinting by technical means (e.g. randomly dither the query-able factors, don't report plug-ins, report always the same OS/version "I am Spartacus", etc) and whatever else you can do to help (e.g. Duck duck go for search, or at least warn people about it). Offer ad-blocking as default (or the setup wizard to chose a matching plug-in), make a simple menu option to stop auto-play videos and animated GIFs, etc.
And FFS stop copying Chrome's every dumb-down-the-user move!