Motorola has now started rolling out the Android 6.0 Marshmallow software update for the 2015 Moto G (3rd gen). The update is 460MB in size and is currently available for the Unlocked version of the device in the US and Canada over-the-air (OTA).
The update brings all the Marshmallow goodies, including Google Now On Tap, Doze mode, App permissions, Do not disturb mode etc. to the Moto G (3rd gen). It also includes Android security patch for this month (December 1, 2015). After applying it, the device will be running on software version 24.11.25.en.US.
You can always check for the latest software update manually by heading to Settings -> About Device -> Software Update. We hope the update also rolling out in India in the next few weeks.