Saijaku Tamer wa Gomihiroi no Tabi wo Hajimemashita. (The Weakest Tamer Trash Picking Journey Begins.)
Synopsis (copied from *****dex):
When Ivy was born into this world, she remembered her past life. Remembering her preincarnation, she strove to avoid strife. But fate curdled at the status check, when kids learn who they are. For she had only one skill - Taming - and not a single star.
Ivy was weak from the start - at most, she could tame a slime. And in her world, most people did not give the weak their time. Only one woman in her village would treat her as her own. But after she died, Ivy got the hint and ran from home.
While on the lam, she met a tiny slime and made Sora its name.
And such begins the heartwarming survival story of a small girl who can tame.
Japanese name: 最弱テイマーはゴミ拾いの旅を始めました。
Publisher: TO Books
Status: 3 Volumes (latest publication date: October 10, 2020)
Amazon link: https://www.amazon.co.jp/-/en/dp/B08L18FSMB (since we don't have LNDB anymore)
Genre: Adventure, Fantasy, Slice of Life
Sounds cute. You caught my interest