Although it is thrusting forward at a rate of 20m to 24m a day, engineers are reluctant to commit themselves to an exact date, given the sensitive pressure adjustments needed as the assemblage nears the surface.
Behind us as we visit the 14.46m cutting face of the first tunnel yesterday, about 18m under Great North Rd, stretches a 2.1km cavern of lined concrete curving back to Alan Wood Reserve in Owairaka, from where the giant ground-eater pushed off in November last year.
Also reaching all the way back is a conveyor belt carrying about 3000cu m a day of soft rock liquidated to a toothpaste-like consistency to be loaded on trucks and dumped at an industrial development site over a disused Wiri quarry.
The air is fresh, courtesy of a massive 2.5m-diameter ceiling intake pipe, and the tunnel is well illuminated by fluorescent lights guiding us to the boring machine.
Not even diesel fumes from a shuttle carrying a 100-tonne payload of 10 concrete sections for the machine to line the tunnel as it goes can foul the air, although there is a dank alkaline smell reminding us to avoid contact with corrosive wash water under our feet.
After being driven most of the way in, we are electronically tagged through a gate to ensure there are no more than 40 people in the tunnel at a time. We are guided on foot the rest of the way on the flat surface of a concrete culvert being laid to carry power and other services before the $1.4 billion motorway link from Maioro St in New Windsor to the Northwestern Motorway at Waterview opens in 2017 with three traffic lanes each way.
Even the culvert - described as a "tunnel within a tunnel" - is a roomy 3.5m wide by 2.5m high. The 40-person limit is to ensure salvage chambers on the machine can provide at least three days of air to their occupants in an emergency.
Once on board the three-decked machine, the roar of 24 motors turning the mining head with its almost 300 tungsten cutting tools at almost two rotations a minute makes conversation difficult. A giant screw rising at 45 degrees from an earth-holding chamber behind the cutting head is dropping grey slurry looking like a bubbling geothermal mud pool on a conveyor belt as the machine's operator, cocooned in a control room, adjusts balancing pressures to keep the tunnel face stable.
Tunnel construction manager Iain Simmons says the machine has a pushing force of 30,000 tonnes, yet only about 5000 tonnes is typically needed "so he [the operator] has to be really careful".
But despite the din and massive power, there is no vibration, which is just as well given that the machine has tunnelled directly below the Mt Albert Pak'n Save supermarket and Oakley Creek at depths of up to 45m.
Mr Simmons says pressure will have to be eased off as the machine edges its way to the surface. He is blase about the prospect soon of breaking through a portal built in a trench next to Waterview Primary School and an embankment which will lift traffic to a three-level interchange for which support structures are already towering 20m above the Northwestern Motorway.
For him, that will simply signal the start of four months of manoeuvring the tunnel-boring machine around in a tight trench so it can start digging its way back to Owairaka.
Once the machine is fully under way on its return journey, after a two-phase turnaround operation, the Transport Agency's Well-Connected contracting alliance will begin drilling 16 cross passages between the main tunnels to provide motorists with escape routes in emergencies.
Although the second tunnel is expected to take only until about next September to dig, there is plenty to be done - including building venting towers at both ends - before the full 4.8km Waterview Connection - half of which will be surface motorway - opens in 2017.