Yikes. Not a good situation there. But at the same time, good for you for trying to effect change rather than jump ship immediately, that's good for public health :)
The fact is if you have poor culture at the very top of the company they don't often learn the lesson of quality until they finally have that bad recall/fda action/etc. But here are some thoughts if your company ends up being willing to embrace quality as a culture.
1. Make sure you are respected first.
No one is going to take quality culture, preventative food safety, etc. seriously if they don't take the person leading it seriously. This is true for personal safety, lean ideas, or really any culture change. Make sure you're not on any kind of quality high horse, and make sure you're making contributions that are relevant and help the floor and supervisors, rather than impose burdens. Examples would be anywhere where you can streamline quality checkpoints or bring in equipment that improves food safety while also increasing efficiency.
Common QA mistake: When working in an environment where a "compliant" culture isn't in place, don't cite regulations to make your point. No one wants to make change because the government says so (especially if they aren't enforcing it), and no one wants to do it to make your annual audit easier. As far as they're concerned audits are your problem once a year and because it's hard for you you want to make it theirs every day. Demonstrate the need for change based on risk to products, people, and business.
2. Prioritize, and let it go
In tandem with #1, unless you have an obvious high-risk product for bare hand contact or hair, let some of that stuff go. We know it's important, but CCP's, QCP's, and sanitation are the big ones that you need to use your "good will" currency on. Don't spend all your patience and points on forcing bangs under hairnets, immediately breaking down that cardboard, etc. And if it's getting bad, make your production guys enforce the small stuff so it isn't all coming from quality. You have bigger fish to fry and a limited amount of points to cash in.
3. Data, data, data
Start getting statistical verification of how you're doing as a company (complaints, defective products, production paperwork errors, sensory failures, mispicks, # of rags left on the floor at the end of the day, disposal costs, time cost for equipment breakdowns).
Lack of quality culture is based on observed cost-benefit. Without data, everyone flies by the seat of their pants and dismisses your concerns with "It's not that much product, we produce a ton of okay product", "it just happens sometimes", or "it wouldn't be worth it for how often it actually happens". Half the time issues don't go away, we just get complacent with them. As a new employee you didn't bring in any of that complacency with sub-par products or food safety risk, and you have to bust some chops with data.
Data also provides a tool to those people who do want to support a quality culture, but haven't had any compelling evidence to disagree with their peers.
I'm a big fan of the ADKAR model for supporting change (and of this graphic detailing what happens when any one component is missing: https://s-media-cach...bf9f8b9986.png)
Here's a limited piece of what you can directly do as a QA manager to support ADKAR.
Awareness of the need for change: Data, data, data
Desire to participate and support the change: respect, focusing only on one problem at a time (I know, it's hard when it feels like an imminent food safety threat)
Knowledge on how to change: Come with multiple solutions or a goal oriented request (What could we change that would get the dirty mop bucket out of the room during production?), demonstrate that changes work with: data, data, data
Ability to implement required skills and behaviors: Volunteer to train employees on new procedures, and change your quality program to make it easier. Maybe you can replace that titration kit for a rapid test method? Maybe you can make a checklist?
Reinforcement to sustain the change: Persistence is key on your ONE issue you're fixing. You may have changed the procedure, but unless they're doing it without help for at least 60 days, you don't get to move on to your next project yet. And if you throw it out there, move onto the next shiny and hope it will stick, it won't.
Ultimately you'll need to decide if your company can do it, because QA is hard and it's only harder if your efforts aren't recognized as beneficial to the business (did I mention data?). Make sure you can do the job ethically and legally and see what change you can effect, but know your personal lines and be ready to walk away from a bad situation.