I am sure you’d not be fired. You can’t be expected to know all ins and outs the very first week. It’s an old established company and they built their spirit, which might not be your style, but you can’t possibly know! It takes a minute. If it becomes a pattern, then it’s a different story. But I’d not worry about being fired. Not happening

I don’t think you could or should quit right away. Good cause is impossible to prove in this case and I am sure you’d not get unemployment after quitting a job in few days after being hired. I don’t see that happening.

Having said that, if you do not think it’s a good fit, there is no harm in looking for a different job. Plenty of people quit jobs soon after being hired if they find out it’s a bad fit, but you gotta find something else first. Perhaps looking into being a consultant, it’s more solitary job I’d think.

Personally I’d give it time to see how the company runs and not do or say anything drastic. Nothing wrong with being assertive. I am certainly not a wallflower so I don’t suggest people become one. You need to be strategic about it though.

You can do it.