Before Kaguya ate the fruit, there was no chakra at all, as it all lied within the Chakra Fruit. Kaguya after eating the fruit is the first person to have chakra (within that world as there are more Shinju's in the other dimensions) and Hagoromo was the first person born with chakra (Hamura is his younger twin, which means he is second).
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Kaguya's chakra is stated to disperse into Hagoromo and Hamura (their chakra is directly from her):
↓ The birth of Hagoromo and Hamura. Kaguya's chakra had become dispersed
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This is directly canon and is stated in both the Manga and Databook.
Still with me?
Next up, is that Hagoromo spreads chakra across the world....
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This same chakra is called Kaguya's chakra:
'Mankind, endowed with Kaguya's dispersed chakra.' And by logic, considering Hagoromo's chakra is Kaguya's, and he spreads it through the world, obviously that same chakra equates to Kaguya's.
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'Progenitor of
all chakra.'
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All chakra 'here' is stated to be the Shinju's (Kaguya's).
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Kaguya says chakra is only hers. Then she states she'll blend chakra into
one once again.
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Sentence structure and logic dictates that she's saying all chakra originally lied together in one, and that she's trying to achieve this once more. Of course you'll probably deny this without a single Manga scan or Databook entry backing you up as is your habit