You have to stand in your receiving rectangle for the service. Does this mean that you cannot leave it until you've properly received and sent back the shuttle?
Until the service has been struck, a part of both of your feet needs to stay on the same spot on the ground (law §9.1.4).
Notably, this means that the rest of your body may be well outside the rectangle. For instance, top-level Mens Doubles players usually stand just after the front service line and have their racket extended forwards in order to attack the service as early as possible:
After the server has hit the shuttle, the receiver is free to move across the whole court. The only restriction is that the receiver's partner may not hit the shuttle. As you can see top-level players are very quick and take short serves well before the service line: