this one is so good but it's more of a heartbreaking found family than cutesy.
the 1st chapter's vibe reminds me of To Your Eternity. (/TДT)/
https://www.mangago.me/read-manga/echoes_of_footsteps/
meanwhile this is very popular... atp, i think everyone have read this.
https://www.mangago.me/read-manga/papa_wolf_and_the_puppy/

any manhwa/manga where a guy takes care/takes in some child? something like on my way to meet mom or gintama?