Whenever I start a new role in a new organization, I like to place an emphasize on four main areas in the first few weeks: allow me to introduce you to the four P's of starting in a new role.
First and foremost, you have to get to know your colleagues. Always make an effort to be friendly, always accept lunch invites, and try to get to know people through common interests or hobbies you might share. Nothing of any significance can ever be achieved in an organization without the support of others. In my mind, people are the most important P.
Every organization has them, love them or hate them, you have to learn the processes from booking time off to gaining budget approvals. Ask for any supporting documentation early on and study it, but remember your new colleagues can also help you with navigating processes, but be careful not to distract or annoy them too much with questions!
Next up we have products, which is the core of the organization's business. Initially you need to learn the products well enough to be able to communicate with colleagues, but later on you will need to talk to customers fluently about the products who will be a lot less forgiving of your knowledge gaps. Spend a lot of time studying the products.
Finally we have projects, and as projects encompass all of the other three P's, I have left this until last. You will need to focus your time on the projects you will be involved in, meet the stake holders, review the requirements and schedules, and finally do a health-check to determine if the project is presently on schedule or late.
Starting a new role in a new organization is exciting and challenging, but with a little structured approach to how you boot-strap yourself into the role, it need not be overwhelming.