How To Quickly Turn Off Audio On Nexus 6P (Android 7.1.1)?
Setting short notification sound should be the fastest way. You can also consider flashing a custom ROM based on stock android 7.1.1 which enables you to mute ringing by pressing volume button. And a lot more.

Video review of AICP ROM



Setting up root and custom recovery on Nexus 6P

AICP ROM 7.1.1 for Nexus 6P (officially maintained with daily builds)