Missionary James Evans developed a romanization for the Ojibwe language in around 1830 AD, but found that Ojibwe students had difficulty switching between the two very different mappings of Latin characters to pronunciation. Inspired by the stunning success of Cherokee a few years earlier, Evans started to develop an Ojibwe syllabary, but his superiours were hostile to the idea, as it ran counter to their goals of assimilation. Evans was not allowed to announce his syllabary.
In 1840 AD, he was redeployed into an area of Manitoba that spoke Swampy Cree and where he had superiours who were supportive of his ideas. He dusted off his Ojibwe syllabary and adapted it a bit for Cree.
Evans found inspiration in three different writing systems from three different continents: Cherokee from the USA as mentioned above, Pittman shorthand from England, and Devanagari from India.
Evans’ syllabary was an abugida, which he was familiar with as he had previously learned Devanagari, one of the many Brahmi-derived writing systems of India. The shapes Evans used for the consonants which started syllables are very similar to the corresponding Devanagari syllables.
Cree also needed consonants at the ends of syllables, and Evans derived the terminal consonants from Pittman shorthand. They aren’t exactly the same, but they are very close.
Something else that Evans took from Pittman, and one of the striking features of his syllabary, was rotation. In Evans’ script, you change a syllable’s vowel not by decorating it with extra lines, but by rotating or flipping it. Rotating a syllable ending in “-a” to the left by 90 degrees turned the vowel into a long “-e”. Flipping an “-a” syllable vertically gave the corresponding “-o” syllable.
Evans gave his script to the world, and the world took it and ran like hell with it. Like happened when Cherokee was introduced, literacy amongst the Cree zoomed up in only a few years, surpassing their white neighbours’ literacy. White folks got a bit nervous about the Cree’s literacy for a time; the Hudson’s Bay Company actually refused to import and sell a printing press to Evans. Evans had to resort to building a printing press himself.
Evans’ script was not only popular with the Cree. The descendants of Evans’ Cree syllabary are used all across Canada to write a large number of First Nations languages, and to a lesser extent in the USA.
Postscript: It is quite possible that the abugida was only invented once, in the form of either Kharosthi or Brahmi. One of those two clearly spawned the other. All other Indic abugidas, past and present, are unambiguously descended from Brahmi. All the Canadian First Nations syllabaries are unambiguously derived from Evans’ Cree syllabary, which was clearly influenced by a Brahmi-derived script. The only other abugidas in the worlds, past or present, were Ge’ez (whose vowel markings showed up so much after Brahmi-descended writing systems became widespread that it is quite likely that the Ethiopians got the idea from the Indians) and a few forms of shorthand (who might have gotten the idea from Indic scripts).