Irresponsible main lead looking after kid for whatever reason.

The Great Show - Korean drama, haven't watched it. Aspiring politician discovers that he is the father of an 18-year-old girl from a long-ago affair. Her mother has died, and she has sole responsibility of three younger half-siblings.

https://mydramalist.com/33369-the-great-show

It's an older J-drama and it's a group who end up looking after a kid.

Runaway - Aisuru Kimi no Tame ni