How do you influence product roadmap when big picture product vision hasn't been established and there are continuous changes?
Don't bother. Run the other way. Pardon my language but there's no influencing in this situation, it's just a pissing contest.
Why work somewhere that's optimizing for activity vs. outcomes? A big picture vision (can be at the corporate or company level, not product) is absolutely necessary to steer direction. If it hasn't been established, then step 1 is crystal clear. Do step 1 before anything else.