I'm a freelance product manager. This means I regularly have to understand new products very quickly. This is my framework to get depth and width quickly.

Company Vision

Why does this company exist?

e.g. DuckDuckGo: "Your personal data is nobody's business."

Company Strategy

How does this company choose to achieve their vision? Which choices have they made?

DuckDuckGo: Provide tracking-free online browsing tools

Product Mission

On the product level, how does the product fit into the company vision & strategy? Which parts does it address?

e.g. DuckDuckGo Search Engine: Search the web without being tracked.

Product Strategy

Which choices have been made to achieve the product mission? How does the product make money?

DuckDuckGo: private ads on our search engine

Product Goals

Which are the defined goals, KPIs, & metrics?

Monthly Searches & Downloads, Average Rating on App Stores

Epics / Features

Which features have been implemented? Which features are they working on and are thinking about?

private relay email

Roadmap

What are the priorities for the next weeks & months?

Once I collected answers to all these questions, I have a very good understanding what the product is about, priorities, and also what they might be struggling with.

Note, that not all questions might be answered. Or you might get conflicting answers. These are usually the points I start working on right away.