From man’yōgana to hiragana
Before kana, Japanese writers used Chinese characters for their sounds as well as their meanings. This phonetic use is now called man’yōgana. Over time, flowing cursive forms helped shape hiragana: the character 安, used for the sound a, became あ.
Sources: Encyclopaedia Britannica: Kana · A (kana), with references. Character paths from KanjiVG.