Papua is the SE "third" of the island; the NE third was
Papua is the SE "third" (or fourth, I suppose) of the island; the NE third/fourth was (historically) "NE New Guinea."
Germany claimed NE New Guinea in 1884; the territory also included the islands (historically) known as New Britain and New Ireland, and the northern Solomons; they purchased the Spanish claims in Micronesia (other than Guam) in 1899.
An potential POD would be the Samoan crisis in 1889; if that had turned into a shooting war, than presumably the US might have taken possesion of the German territories in the Southwest Pacific.
Likewise, if Diederichs had intervened in the Phillippines in 1898, there's another possibility; finally, the Venezuelan Crisis of 1902-03, had it evolved into an actual conflict between the US and Germany, offers a third possibility.
Best,