Having read your description, you could be wasting your valuable skills, experience and time on them. I had a job like that many moons ago, in the end they took my efforts to get things organised (what I was hired to do) as a personal affront. They couldn't organise a whatsit in a brewery and any attempts I made to create structure were futile.
IME when the leader is chaotic and is not receptive to change, its a culture and mindset that percolates down through the organisation. After all, if the boss does it why shouldn't everyone else.
That said, a couple of things that stood out from your description - just thoughts:-
1- it is very early days to launch into too much change, even though it is what you were brought on board to do. It might be worth (if only to satisfy your own professional standards) to jot down some priorities around what you feel needs an overhaul, as a 3, 6 month and 1 year plan (like a project plan to propose to the boss. That may take you quite a few weeks to do an audit and create that proposal as a business case.
Making systematic and process improvement changes requires an intimate knowledge of that organisation, and I expect you'd agree you don't yet have that. How realistic is it to change to the extent you want to?
2- could you create your own induction plan? It sounds like a lot of self help will be needed, they don't have mature processes, you already know that, so you have to work in their imperfect world for the time being at least.
Just wondering if you can "be the change you want to see" ( as Ghandi would say) whether that could be the starting point.
Do you see much resistance in the camp? I think the only big threat would be if you have a person/people who are vehemently resistent and could cause you major grief with your boss about change....
Alternatively if you feel it is a completely lost cause, then get out while the going's good! 