Relax, OP. They wouldn't have hired you if they didn't think you could do it.
It's very common to feel nervous in a new job. Everyone has had (and usually hates) the experience of being the new kid, having to ramp up etc. Just accept it. Take people to lunch or coffee. Give yourself "on-boarding" time and do get-to-know you meetings of 1/2 an hour with teammates. Ask them about their jobs, ask for pointers.
Also realize, it's going to be several months at least before it feels like old hat.
Lastly, spread around your questions. Esp. in the beginning, when you're in meetings, just take notes and then look up the answers or ask people privately afterward to explain things in more detail. You have a grace period for a little while as a newbie--just use it to ask questions and learn more.