“Prisencolinensinainciusol”
American sounds like “Prisencolinensinainciusol” according to Adriano Celentano who recorded an Italian pop song constructed from American-sounding syllables.
from the Wiki page: https://en.wikipedia.org/wiki/Prisencolinensinainciusol
The song is intended to sound to its Italian audience as if it is sung in English spoken with an American accent, however the lyrics are deliberately unintelligible gibberish with the exception of the words "all right".
I'd go a step further and say "all right" (the only recognizable phrase) is more like "awwrite", which is a meaningless idiom in Americanese that simply acknowledges that something was heard, or a low-key confirmation that something was understood (uh-huh, OK, yeah-yeah).
Extrapolating: I suggest you find some of these phrases, meaningless idioms that she might say often, and make it a personal quirk catchphrase that she is saying unconsciously, and then do a reductive interpretation of the syllables in the way she would say it.
"You get me?" – Yugit mie
"And what..." – Ant Dwot
"Oh my god!" – Ommigawd
Satire
If 1,000,000 years (an awfully long time) is a hint that this is satire or comedic, you might pick an anachronistic phrase that suits the theme of this future along the lines of Aldous Huxley's satirical Model T worship in Brave New World.
Huxley combined (probably) the Catholic gesture 'sign of the cross' with Ford's Model T to suggest a society that views industrialization on the level of religion. A Model T no longer stands for progress, so that metaphor is lost today but was well-understood at the time.
Something like a meme or advertising jingle having been elevated to an idiom in her timeline.