When to leave a job early on?

A month ago I started a new DE role at a very-large broadcast company you all have probably heard of. I have since found out that the team is possibly the poster-child for disorganised mobs. They've been accruing technical and personnel debt for almost a year, been burning developers/engineers to the ground with very little support and riding a rolling tide of consultants, coders coding whatever they feel like, hands-off management, little to no inter-team communication, requirements manifesting with little process with no option to get feedback, waterfall planning 2+ years ahead, no documentation or testing on the systems they're building etc etc.

Proactively, it would be a good opportunity to help build positive change. But in the role I'm in, I am not immediately empowered to do so, and I believe that the personal cost it would require is significantly more than serves to be gained.

I am thinking of handing in my notice after only a month, my reasoning being that it's mutually beneficial for myself and the team to part ways, I don't spend 1.5+ years of my life 'doing my time' for optics, and they can get a more invested and productive employee. But I'm worried about the optics/fallout for future job searches.

I'm curious to have a discussion around on what people feel about someone leaving a job that's clearly not the right fit so early after starting? What experiences have others had in tech with similar stories? Both good and bad, and general opinions. Years of experience, region, industry info would be helpful.