We teased this possibility on Friday, but Google has gone ahead and posted June’s security patch for Nexus devices. When we say “posted,” that of course means both factory images and OTA .zip files, so you should have no problems updating immediately without having to wait for a prompt.
As of right now, we have Android 6.0.1 files for the Pixel C (MXC89H), Nexus 6P (MTC19V), Nexus 5X (MTC19V), Nexus 6 (MMB30J, MOB30M), Nexus Player (MOB30M), Nexus 9 (MOB30M), Nexus 5 (MOB30M), and Nexus 7 2013 (MOB30M, MMB30J).
You can grab each image or OTA file at the links below. For instructions on how to flash a factory image, here you go. For instructions on how to flash an OTA .zip file, here you go.
Links: Factory Images | OTA .zip Files
UPDATE: If you are curious about the vulnerabilities that were patched, you can read the June Nexus Security Bulletin here.