What are some tried-and-true "quick wins" or early successes that you targeted to quickly demonstrate your value when taking on a new role or joining a new organization?

Winning over the people is often the first order of business when taking on a new role. Using probing and listening skills to show people above and below on the organization chart that you are interested in their point of view and their challenges. Understand them professionally and personally, "break the ice", which then allows for more meaningful sharing of the real issues as trust develops. Become recognized early as someone who is curious and interested, this will position you for later if changes have to be made and mountains have to be moved.

Prepare your 30/60/90 days imprpvement plan where you identify low hanging fruit opportunities / quick wins that you can target in less than 3 months.

The best investment in time that a new entrant can make is getting a good understanding of the landscape and history of the function. Jumping to execution (unless a fire is burning and action is required) for a quick win is a mistake. Unless you understand what constitutes a win and how the role adds value in a way that increases the company's competitive positioning, the win will likely be just a tactical win. It will delay the larger win of setting up the appropriate structure, goals, and processes that will lead to ongoing success. Quick wins are overrated, lasting success is what should be focused on which means spending a lot of time understanding where long-term value can be added which also means the work is tedious and lacks excitement in the short term until people, processes and tools are mobilized to achieve the longer term vision.