Do you think the "saw" is really implied? Because honestly I don't.

(CK's deleted comment)
>Perhaps one of these.
>
> One day in October, when Sadako awoke, her mother was crying.
> One day in October, when Sadako woke up, her mother was crying.
>
> If the "saw" is implied, then maybe, "she found her mother crying" or "she noticed her ...."

CK, you shouldn't delete your comments too much. They often include important suggestions.


When I was in high school, my teachers tended to make us translate this kind of sentence as:
One day in October, Sadako woke up to find her mother crying.

I don't know if this is the best translation of the Japanese, but if I were to translate this English into Japanese, I'd write the exactly same sentence as mookeee-san's. I don't usually say 見つける or 発見する in a situation like this.

Here are two example sentences from 『ウィズダム英和辞典』 with very natural Japanese translations.
I arrived home and found the house empty.
帰宅してみると家にはだれにもいなかった。
She woke to find a man (standing) by her bed.
彼女が目を覚ますとベッドの傍らに男が（立って）いた。

Thank you, tommy_san. I think my experience with Japanese just isn't enough at this point to pick up on some of the small nuances, the things left unsaid.

Question:
Does the English "One day in October, when Sadako awoke, her mother was crying." only tell us that the two things happend at the same time? Is it possible the Sadako didn't notice her mother crying?

Yes to both. But the way it is now, there is no possibility of that.