Installing Nest Thermostat. C Wire not hooked up inside furnace
Add it to the wirenut with the fat blue wire in it

On a typical split-system with air conditioning, there will be a two-wire cable running out to the air conditioner with one wire connected to the yellow Y wire and the other wire connected to C; this cable carries the call-for-cooling signal from the indoor unit to the compressor unit's contactor.

As a result of this, we start our trace at the Y wire, and trace the wire connected to it back to the outdoor unit's control cable.  From there, we can deduce that the other wire must be connected to C in order for the air conditioning to work, so we can simply add the blue C wire going to the thermostat to that wirenut.  This is confirmed by the fact the wiring diagram you posted shows that connections to the secondary-side ground (C) are all blue wires, and the wire nut in question has a fat blue wire going into it.