Is it possible to add a LAN cable to an apartment pantry?

The area marked with a red V is the pantry, and I'm thinking about
turning it into a computer room..
The interior design company says it won't be easy since we've already moved in ㅠㅠ
The main communication terminal box is in the blue area next to that space,
so I was wondering if anyone has tried this before ㅜㅜ