Daisy was passing by a church on the baptism day
https://mangadex.org/chapter/49cbe289-5074-4628-8112-92204ec73b79/22
And heard the girl's parent discarding her for having 'useless' alchemist job despite their family being a martial one.
So the new girl is 5 years old, her name is Lily.
(Daisy by the time she open her store is at least 10)
She's actually niece of the knight commander
https://mangadex.org/chapter/e525bbe5-c3de-4ce3-850a-fc8e8ca86c85/14
The knight commander came to apologize for his stupid brother, but being family his resemblance to her father caused Lily to flinch in fear.
Understanding this, the commander ask if Daisy would become Lily's teacher in alchemy, and for her family to adopt her.
Because in the future when Lily start to make name for herself, if she's adopted by commander the trash father might come demanding her back.
So her being with unrelated family would make it harder for him to pull that stunt.
Lily turns out to have pretty high potential, having born with good five senses then get blessed by a god even more.
She can see faeries without having green spirit king's blessing.
She succeed in making potion on the first try by tasting Daisy's successful one then brew until she 'got the same flavor'
She could hear voice of stone/metal to find compatible ones.