This is a really weird exception, sorry. You've kind of learned these reading, but they're like... weird variations of them.
Take the さ from 早速, the おつ becomes おと, and then the 女 kun'yomi め (hey that one's normal!). And you get さおとめ. You might need to just memorize this one.
Long ago, women who planted rice seedlings were called Saotome or Ueme.