There might be some confusion as to what the word "borrowed" means. The usage of 「無」 to mean without is a rebus borrowing. From Wikipedia:
An example that illustrates the Rebus principle is the representation of the sentence "I can see you" by using the pictographs of "eye—can—sea—ewe".
That is, to ask how the sentence
I can see you
originated from the pictures
is an incorrect question.
If it is difficult to see how the glyph evolved into its current form 「無」 (Baxter-Sagart OC: /*ma/, without), that is a more tangible query.
Start from a rather vivid picture of a person 「大」 holding a bunch of adornments in each hand, doing a rain dance*.
Complexify the adornments, maybe into something highly resembling a sound hint 「某」 (/*məʔ/).
Omit the shape of the person 「大」.
Then finally, abbreviate the bottom of the character into a few dots.
Dance is written with the derivative character 「舞」, by adding semantic 「舛」 (picture of two feet).
*The nature of the dance being linked with rain is from the extensive number of fragments where the character 「無」 is found with the character 「雨」. E.g. 《甲骨文合集》12828: