Coming from a Business Systems Analyst / QA Analyst and now a SQL Developer with 10+ years exp in Software Development, I may offer some advice on how I maximize my opportunities on a new workplace. I apply these principles in everything that I have to learn new. Not just a new job, but any new technologies or challenges that I come across with. There's a lot more to be said but these are the ones that helped me the most. In a matter of weeks, I am caught up to speed with the most important processes. Of course, not everyone here may agree.
Mimic actual business process in DEV/Test Enviroment Grab the most common business practices and processes and try to do them on your own with the mindset of a user. Call / interview critical users that will give guidance to what they do day to day. This will give you a perspective on the limitations and strong functions that works for the business. This has helped me tremendously to understand "what works" vs "what doesn't work" vs "what can be improved in the future". This has forced me to map out every business requirement/process to understand the blood flow of a business.
Test in Dev Envionment Play around in a mirror test environment to get familiar of IN and OUTS of the major systems. This has allowed me to understand components, functions, batches that crucially support our business. I spent my first week doing this while reviewing documentations and interviewing key employees.
Open / Review previous projects that were already deployed I review projects that were already completed by my team and understand their accomplishments with their perspective. I interview my team and ask them if there's anything that they could have done differently or improved on their project. Key players that helped and key players that they had to learn to work with.
Take advantage of low hanging fruits Get your feet wet in the first day by taking low hanging fruits task in your new environment. Whether its a simple update, code change, test, simple query, take it. I would suggest that you ask your new co workers if there's anything you can do to help them. This has allowed me to get an airplane view of my own internal team and what they do that makes them successful.
Good luck and CONGRATS. It's a big accomplishment. Enjoy your team :-)