We try to have prototyping/design finished by the end of the first week - in other words, tomorrow
Last year, our robot design incorporated several possible stopping points short of fully finished that would have given us various levels of capability. Because of that, a few people could work on prototyping a little longer on the more complex actions, while everyone else started on the drive train and other parts. This year, we don't really have that buffer, so we're really focusing on getting everything we need to prototyped by the end of the day tomorrow!
Of course, this may vary for teams... But you'll find that the quicker you can do your design and prototyping, the more time you have to actually build the robot, and the more time you'll have to practice driving it around - and that last part is incredibly important this year.