The University of Waikato has an interesting and detailed narrative on New Zealand's natural history, based on its geological and fossil record. I'll summarise some of the main points here. (A reminder that this whole exercise is aimed at better understanding the circumstances surrounding the appearance of a non-therian mammal fossil in the south of NZ.)
Speaking specifically about the parts of New Zealand that are above water now, parts of NZ first rose from the sea in the Mesozoic era (dinosaur times), in the Triassic period (250 million years ago to 201 mya). Fossils are found in this period of early forms of kauri, rimu, and kahikatea trees; no terrestrial vertebrates.
In the Jurassic period (145mya to 201 mya), NZ was uplifted as part of a larger land mass ("Tasmantis"); the narrative strongly implies it was connected to Gondwana. In any case, it says that due to NZ's subsequent isolation, it is likely that this point saw the arrival of "archaic frogs, large land snails, tuatara, and peripatus".
Under the Cretaceous (65mya to 145 mya) heading, it mentions a single vertebra of an upright carniverous land dinosaur. It also mentions waterways developing around 120mya between Gondwana and the land mass that included NZ. A consensus from other sources is that that split was final by about 82mya. The dinosaur extinction event was 65mya; the iridium boundary marker has been noted in NZ.
Other points of note:
- Oligicene epoch (23-37mya): two thirds of NZ was submerged (it notes the continued survival of frogs, tuatara, snails, peripatus and ratites (flightless Gondwanan birds);
- Miocene (5-23mya): bat, gecko and takahe ancestor appeared from Australia...
And we're back where we started: the SB mammal from around 19mya: Miocene, but non-therian. Appearing from Australia relatively recently (despite no equivalent fossil found there), or surviving from Gondwanan days.