More will follow regarding using a scheduled flight.
Now for discussion on potentially using a scheduled flight.
One of the key points to remember about using a scheduled flight, is that such a flight would need to be a direct flight. If the aircraft had to do an intermediary stopover somewhere prior to traveling on to NZ, it could (and likely would) be detected as 'odd' and dealt with either in the air or on the ground by the stopover nation. As a side note, Australia is the most likely stopover for non-direct international flights to NZ. IMO it is unlikely that Australian personnel would not detect something suspicious about an entire airliner (passengers and aircrew) that was being used to transport a group of people and weapons to launch an assault on NZ, report their suspicions or otherwise take action.
I have looked at lists of direct international flights to NZ, and only one seems to be a possible candidate, and that is a daily flight from Kuala Lumpur, Malaysia to Auckland, NZ on an A330-300 that can carry up to ~283 passengers + aircrew. IMO the security forces of other nations with direct international flights to NZ are too capable, and have too much accountability, to permit the activities needed to enable the airliner cabin to be loaded with weapons and munitions for the passengers and aircrew. I just cannot see a scenario where a group of ~300 people were permitted to board an airliner loaded with weapons could occur in the US, Canada, Australia, Japan, China, or Singapore. Also none of these nations have active insurgencies or volume traffic to or from areas with such insurgencies.
At present, this leaves only that single daily scheduled direct international flight from Kuala Lumpur to Auckland which could bring in ~300 attackers in a trip to start a campaign to seize control of NZ. The first objectives would have to be to establish either a landing zone for flying reinforcements in, or a beachhead to land troops aboard vessels. Frankly, I do not believe that 300 attackers armed with small arms would be enough. Within the Auckland area there are over 1.5 mil. people, plus nearby NZDF bases with RNZAF, RNZN, NZ Army, and NZSAS personnel.
I do not see how 300 such combatants could effectively take and hold even just Auckland Airport for more than a short duration after having flown for 10+ hours.
Options to get reinforcements into NZ would be limited, as would the time the attacking force had to get reinforced. These would amount to either additional unscheduled NZ-bound flights with the risks of detection detailed in the previous post. Such reinforcing flights would need to already be en route (most likely almost at the airport) prior to the scheduled flight landing as a security cordon to contain the attackers at the airport could be setup fairly quickly with potentially as few as five barricades. In addition, quick thinking personnel at the airport could quickly and easily take the runways and taxiways out of service temporarily. All that would be needed is for a few large, heavy, or hazardous materials vehicles (fire apparatus, construction vehicles, fuel trucks, etc) to be driven out onto the runways and taxiways and then parked and disabled. An impact between a fire or fuel truck and an A330-300 traveling at 137 kts might not destroy the aircraft, but I am certain the crash would render the people aboard in no condition to engage in hostilities immediately.
OTOH if the plan was for the ~300 attackers to establish a beachhead for reinforcements that way, that too is very problematic IMO. First they would need to get clear of the airport itself with their weapons and equipment, while the alarm is being raised about the attack. Immediately afterwards they would need to secure sufficient transportation to move enough attackers and equipment to where they plan on establishing their beachhead. Meanwhile the ship(s) carrying reinforcements would need to already be almost at the beachhead. As a side note, much earlier in this thread IIRC there were a series of posts discussing a whole host of potential problems that a hostile force would encounter if they were to attempt to use a merchant or cruise vessel to land a body of troops on NZ.
From what I have been able to determine, the best place to establish a beachhead for reinforcement by sea would be somewhere along Quay St in Auckland so that reinforcing ships could have a wharf to dock alongside and unload personnel and equipment. If this is correct, then it would mean the attackers would need to drive across the metro Auckland area from the airport and arrive in sufficient numbers to seize an area for the ship(s) to dock and have the reinforcements disembark, and hold that area until it was no longer needed.
Aside from the difficulties that would likely be encountered getting attackers from the airport to the area around North, Princess and Queens Wharf, that area is also almost directly across the harbour from the Devenport Naval Base. Depending on what vessels were in port at the time of the attack, it is quite possible that the reinforcing vessel(s) and/or the beachhead itself could come under attack from either vessels deploying from the base, or from vessels within the base.
The basic conclusions I have reach based off the information I have come across is that without a hostile nation-state able to deploy and sustain an amphibious assault task force, there is no practical means for sufficient forces to get to NZ to contest control, never mind conduct an occupation.
To use the invasion of the Falklands Islands by Argentina as a rather poor example, consider this. The British and Falkland forces that responded to defend the islands had a total strength of 100-110. These were composed of personnel from the Royal Marines, RN, FIDF (a volunteer militia) and civilian volunteers, from a total population on the island of ~1,800. The Argentinian invasion force had ~600 troops, including marines landed in Amtracs, special forces, and tactical divers. The Argentinian force also had naval components including a sub and a
Sheffield-class destroyer. Also the Falkland Islands were within the range of land-based Argentinian strike aircraft, only being ~500 km from the mainland.
The reason I say the Falklands War is a poor example is that New Zealand is considerably (20x) larger, has a much larger comparative population ( ~2,300x), and NZ is more remote (3x) with ~1,500 km being between the closest points in NZ and mainland Australia. Also there are basically only two nations with land-based strike aircraft which could reach NZ, namely RAAF aircraft from Australia, or long-ranged USAF strike/bombers.
One of the other important considerations to keep in mind. It would require something very serious and/or strange for either Australia or the US the be either unable to unwilling to provide NZ with direct military assistance in the face of a potential invasion. While I do not deal in certainties (Death and Taxes aside) the likelihood of the various conditions and events occurring around the at the right time and in the proper sequence to render such attack plans potentially viable is IMO very remote.