What should you aim to do in your first month and your first quarter?
In the first month I would aim to meet with my key stakeholders, understand some of their recurring pain points and try to address 1-2 of those pain points right-away (<30 days) to develop trust. This is likely to be a balancing act since you want to be careful about unintended consequences and not committing to a short-term fix that could create potential issues in the long run.
From there on out, I would focus on meeting with extended (cross-functional) stakeholders and understand the political landscape within the organization i.e. where does the decision making lie, who can help/support your priorities, who do people trust, where are the potential landmines and start to develop those long-term relationships.
In your first month, you should not only be building a great understanding of the product and business, but also what the company's go-to-market looks like across the business. Aim to understand the relationship between your key GTM functions (Sales, Marketing, Customer Success) and identify opportunities to build connection both within and across these functions while building relationships with each of these teams.
Over your first quarter, you should start to build out a list of priorities focused around:
Breaking down potential silos between go-to-market functions (in particular Sales<>Marketing and Sales<> CS) - are these teams talking to each other and understand how their work relies on and impacts the other functions?
Identify core KPIs across functions and assessing if they are the right ones. But in particular, do you have success metrics that help you understand the flow of the customer journey? For example, do you have a metric that helps you understand if Marketing is driving quality leads for Sales and they are turning into revenue?
Communicating to leadership where you see opportunities and recommendations to identify gaps in your ops functions across the customer journey.