Being a Product Manager means juggling various topics at once. This becomes easier over time as one develops certain stamina for back to back meetings, sees reoccurring patterns in different situations, or just has a stronger intuition.
All of this is often based on a strong foundation, a cemented base that holds up history, context, thoughts, judgments, and anything else relevant. Building this foundation early is important, as you'll be prone to bias at a later stage.
Therefore, it is of utmost importance to study as much as possible within your first few weeks. Good product managers constantly learn, constantly gather information informally, and constantly listen to the signals their environment is giving them.
Study your product
You must become the de-facto go-to person when it comes to your product. No matter the question, you either need to have the answer or know how to get to it. Use your product. Try to break it. Then fix it. Afterwards, break something else. Study its quirks, see where its performance is lacking. Learn from its winning features, closely monitor features that struggle gaining adoption.
If you have a support team, stay close to them. Learn from their experiences. If possible, do the support yourself. Build empathy for existing users. Pay special attention to support requests from customers that have been using your product for a long time. They might have outlived your predecessor Product Managers. Learn from their journey.
Most importantly, focus on studying by asking questions and not by raising judgement. Don't arrive at a place of business and insult its operators. Stay curious. Replace raising concerns with raising questions. Become the de-facto go-to person when it comes to your product.
Study your market
Who's your customer? Why do they need your product? Where are you in the grand scheme of things? Who are you competing with? Where are they out- and under-performing you?
Don't be naive. The world is full of smart people and sometimes smart people have similar smart ideas. You won't be the only one working on your problems. Observe and learn from the others.
What are customers thinking about your company overall? How much churn and retention does your company have? What are reasons for churning? How much additional revenue does your product get from existing customers? Even if you are working on an internal product, especially for SaaS companies, it's important to know these things. As a Product Manager, you need to understand the business and where it's heading. For your own and the business's sake.
Study your team
Don't just schedule one-on-one calls with your immediate team members. Figure out what drives them. What do they see critical in their current roles? Distinguish product-minded engineers from the ones that aren't. Which team leads tend to dispute product decisions? Which ones accept everything you bring to their attention?
Same as with customers: which team members have been around the longest? Find out why. Learn from their experiences. Learn the dos and don'ts of your company.
All this information is not to play useless games, not to study your team members' mind and soul. It's purely pragmatic. You are going to have to make decisions; choices that will determine who might work on which topics and it's crucial for you and your product that you make informed decisions whenever possible.
Knowing your team and each member's strengths and challenges isn't to leverage it for meaningless politics. It's for pushing forward your product, together, with the sole purpose of generating value for customers and expanding the business. Don't forget that it's the only goal a product manager has. People won't tell you that they don't like talking about the what and the why, but would rather just focus on the how. It's your responsibility to distill as much clarity as possible about your team's dynamics.
Study your management
This shouldn't change your day-to-day life. However, especially in larger product organizations, it won't hurt to know how management works. How are things settled between two conflicting orgs?
On a personal level, who determines aspects about your career? Who decides on your scope, your responsibility, and consequently, your compensation? Understand that the person you report to might not be the one-stop-shop for all your career related questions, which is fine. Be comfortable to speak about these topics with whichever person you deem ideal, but understand that there's a way of doing it. Der Ton macht die Musik.
Among all of the things to study to, this is the least urgent. Take your time and don't be pushy. What you want to be is curious, not nosy.
After X+1 days
All of the above isn't just a one-time thing. It's your responsibility to constantly exercise, gather and interpret information from your environment, and use to to make the best possible decisions for your product.
Keep in mind that information changes over time. A lot of what you'll be doing is based on assumptions, start being comfortable with that. Have empathy with current aspects of your product that might have been built when certain assumptions couldn't be fully verified. Have empathy for the past and be careful when raising judgement. Instead of agreement, you might run into resentment.