The Essential Phone is now receiving a new software update, on the eve of its release in Sprint stores across the US. While technically it isn't the first, the previous ones were only actually seen by people with review units. For all intents and purposes, this should be the first update notification that people who bought the device will come across.
Before you ask - no, it's not Oreo. Essential promised quick Android version updates, yes, but it's too soon for that. Not one non-Google supported device runs that yet.
What this update does bring is the September security fix. The Android version remains 7.1.1 Nougat. The new build number is NMI64C. It arrives over-the-air as a 175MB download, and seems to improve performance once installed (at least in terms of scrolling inside apps or settings, which is now less janky). If you don't want to wait for the update notification to show up, go to Settings > About phone > System updates and force a manual check - it should give you the new release right away.