I can totally see how it could be overwhelming to learn a new team's domain / vertical from scratch. 

My thoughts are: 
1. Get clarity of what's important moving forward and learn by solving a problem. A team may own a lot of things but not everything is important, focus on what's important. This requires proactive alignment with your manager / new hire mentor. 
2. Build a learning agenda - following techniques from @alex chious's answers and build yourself a 30 - 60 learning agenda, carve out time for deliberate learning. Keep in mind that every company / team is different - some have strong documentation, some relies on tribal knowledge, some has good onboarding programs... observe what's effective in your environment to avoid wasting time.