Okay to leave job after a month?

I joined this new job recently, been a month.

Have about 10ish years of experience, and not enjoying the new place. I feel they have hired me prematurely and don't have any real work for me and I am bombarded with stuff, which I feel is intern level / stuff meant for a very junior resource.

The expectation on ownership was very different when I was sold the role, but it doesn't seem like they are in a position to deliver the role for the next 6 months.

I feel they have overhired anticipating scale that they would hit 6 months out (which I am very skeptical they would).

Do you guys think it's okay to leave within a month? Has anyone done that before?