I have a dejavu feeling when reading [What to do about a 11000 lines C++ source file?] post, but I don’t think I can start taking action on my own since I do not have the authority to take action. So I think the first step is to convince people in the organization that big lump of code is bad.
I have a similar situation where there is a single class with 11975 lines of code and every time there are new features, there is a high probability that this class will get bigger and bigger.
You have my sympathies. Any class that is that huge is inevitably breaking the Single Responsibility Principle, making it difficult to maintain.
My best advice is to lead by example:
Your code will shine like a beacon compared to a the legacy code and your team will understand which code is easier to maintain.