We know Takeya Yuki's past is still a mystery, so that's why i will explain her past

My version :

Yuki's parents died when she was little Then finally Yuki becomes an orphan, and Yuki is cared for by people who work in the Church.

And then, When Yuki arrived on a hot summer day Yuki accidentally met Megu-nee at church, at that time Megu-nee was still in high school and aspired to be a teacher at her school.