You may have stumbled on Cat Lady from Alderac Entertainment Games already, a game about cute cats, with cat cards, food for cats, toys for cats, and a cat meeple that is purring around the drafting display. A well recognized flaw of this game was that other people got in your way to interact with the cats. Which is why components to make it soloable have been included in the latest expansion, Box of Treats, released in 2020.
The next coming expansion, Kittens (if you want a cute game cuter add kittens apparently), is also listed as a 1-6 players game on the BGG page. In all likelihood, you will need the solo components of the Box of Treats expansion to make it work, but the good news is that it's that the Kittens are compatible with it.