From this this paper, in an extract authored by one Mr. Sekino (関野) in 1943:
It's a pretty old usage of Japanese. I'd be grateful if somebody other than me could lend a hand in giving a proper translations of things like 用ひ (I assume 用い?) in this text, but I think it has the answer OP is looking for.
From what I understand, they did teach hiragana, but katakana first, and this was used in items such as childrens' books. Katakana was used as a gateway to Japanese grammar and pronunciation, and this was followed by the education in hiragana and kanji afterwards.
The reasoning for this could be down to katakana's greater status historically (such as being used in treaties with Korea and China in the late 1800s). Katakana was once historically the only script, and up until around 1900 katakana-kanji was used exclusively (including in treaties with Korea and China), but nowadays hiragana is by far the more useful of the kana syllabaries. Between 1900~1945, I know that hiragana was used informally (in letters between friends and in wartime posters), but I'm not sure when it was accepted into formal documents, if this was even pre-war.
As for Sayo Masuda, she never received any education in her youth, and post-war Japanese script reform made (and makes) starting with hiragana a more useful tool; probably why she and Japanese children nowadays learn it first. There's also the viewing of hiragana historically as "womens' writing", at least pre-1900s.