The phrase Google Tree appears in St. Nicholas: An Illustrated Magazine for Young Folks from 1898 (starting on p. 35, or p. 49 of the pdf file):
Both madly loved the Lily Maid,
And better to decoy
The other from her, each reviled The little Tailor Boy;
And vowed a most tremendous vow, By the great Google Tree,
Next matinee they would him slay,
And so revenged be.
Google Tree doesn't appear anywhere else in the book mentioned above.
I've found contemporary usage for Google Tree, but obviously, this wouldn't apply to the past:
Google Tree is a life-sized fabricated tree plucked from the ubiquitous software Google Earth. Not quite a replica, the tree is a copy of a copy—a physical experience created from an unreliable digital proxy. - bitforms.art
Could it be used adjectively? Google is another form of the adjective goggle meaning "Of the eye: Protuberant, prominent, full and rolling; also, ?squinting." per the OED.
Could it be a typo/misprint, an invention, or perhaps a hidden message from time-traveling Google founders?
Note: The author also used other real things, places, and terms (mostly Dutch-related) in the poem that might seem invented but actually aren't. For example:
Mynheer Jan van der Swannigan,
Of high descent was he;
His father peddled pepper-pots
Along the Zuyder Zee.
And Zuyder Zee is defined in Wikipedia as:
The Zuiderzee or Zuider Zee (Dutch: [?z?yd?r?ze?]; old spelling Zuyderzee or Zuyder Zee), historically called Lake Almere and Lake Flevo, was a shallow bay of the North Sea in the northwest of the Netherlands.
Thus Google Tree might be something real also.