So is GURPS Deep Star Inspired by the Expanse ?

In short. No.

I hadn't watched the show till well after I decided on what would suit our current play situation best. I have seen the first episode, it was a tolerable Space Opera using some Hard S.F.

Nothing wrong with that as it seems right up my alley but thus far, I find the show to be meh and probably won't be watching it.

That said from what little I saw it would be quite suitable for a GURPS game.